diff --git a/README.md b/README.md
index fdf3c67..6f75eca 100644
--- a/README.md
+++ b/README.md
@@ -45,7 +45,7 @@ grows proportionally to time:
 variance_delta = elapsed * γ²
 ```
 
-This is the standard TrueSkill Through Time model. Pass a `ConstantDrift(gamma)`
+This is the standard TrueSkill Through Time model. Pass a `ConstantDrift::new(gamma)`
 when constructing a `Rating`:
 
 ```rust
@@ -53,9 +53,9 @@ use trueskill_tt::{ConstantDrift, Gaussian, Rating};
 
 // gamma = 0.1 means skill can shift ~0.1 per time unit.
 let rating: Rating<i64, ConstantDrift> =
-    Rating::new(Gaussian::from_ms(0.0, 6.0), 1.0, ConstantDrift(0.1));
+    Rating::new(Gaussian::from_ms(0.0, 6.0), 1.0, ConstantDrift::new(0.1));
 
-assert_eq!(rating.drift().0, 0.1);
+assert_eq!(rating.drift().gamma(), 0.1);
 ```
 
 The type annotation is load-bearing: `ConstantDrift` implements `Drift<T>` for
@@ -98,14 +98,14 @@ assert_eq!(history.log_evidence(), 0.0);
 ```
 
 `HistoryBuilder::drift` is the only way to set a history's drift model; there is
-no `gamma()` shorthand. The default is `ConstantDrift(GAMMA)`.
+no `gamma()` shorthand. The default is `ConstantDrift::new(GAMMA)`.
 
 ### Per-competitor drift
 
 A `History` has one drift model, but individual competitors can scale it.
 `Member::with_drift_scale(s)` multiplies the drift *variance* that competitor
-accumulates, so `s` is in the same units as `gamma`: `ConstantDrift(g)` at
-scale `s` behaves exactly as `ConstantDrift(g * s)` would, for that competitor
+accumulates, so `s` is in the same units as `gamma`: `ConstantDrift::new(g)` at
+scale `s` behaves exactly as `ConstantDrift::new(g * s)` would, for that competitor
 alone.
 
 `0.0` pins a competitor still. That is what makes a **fixed reference point**
@@ -115,7 +115,7 @@ strength, a rating floor, a course difficulty:
 ```rust
 use trueskill_tt::{ConstantDrift, Event, History, Member, Outcome, Team};
 
-let mut h = History::builder().drift(ConstantDrift(0.1)).build();
+let mut h = History::builder().drift(ConstantDrift::new(0.1)).build();
 
 h.add_events(vec![Event {
     time: 0,
diff --git a/benches/batch.rs b/benches/batch.rs
index 2f30794..20bd6c7 100644
--- a/benches/batch.rs
+++ b/benches/batch.rs
@@ -17,7 +17,11 @@ fn criterion_benchmark(criterion: &mut Criterion) {
         agents.insert(
             agent,
             Competitor {
-                rating: Rating::new(Gaussian::from_ms(MU, SIGMA), BETA, ConstantDrift(GAMMA)),
+                rating: Rating::new(
+                    Gaussian::from_ms(MU, SIGMA),
+                    BETA,
+                    ConstantDrift::new(GAMMA),
+                ),
                 ..Default::default()
             },
         );
diff --git a/benches/history_converge.rs b/benches/history_converge.rs
index aff9a0c..f623c37 100644
--- a/benches/history_converge.rs
+++ b/benches/history_converge.rs
@@ -47,7 +47,7 @@ fn build_history_1v1(
         .mu(25.0)
         .sigma(25.0 / 3.0)
         .beta(25.0 / 6.0)
-        .drift(ConstantDrift(25.0 / 300.0))
+        .drift(ConstantDrift::new(25.0 / 300.0))
         .convergence(ConvergenceOptions {
             max_iter: 30,
             epsilon: 1e-6,
diff --git a/benches/joint.rs b/benches/joint.rs
index eb5aff1..e611979 100644
--- a/benches/joint.rs
+++ b/benches/joint.rs
@@ -16,7 +16,7 @@ fn fitted() -> History<i64, ConstantDrift, trueskill_tt::NullObserver, String> {
         .sigma(6.0)
         .beta(1.0)
         .score_sigma(2.0)
-        .drift(ConstantDrift(0.05))
+        .drift(ConstantDrift::new(0.05))
         .convergence(ConvergenceOptions {
             max_iter: 30,
             epsilon: 1e-10,
diff --git a/benches/scored.rs b/benches/scored.rs
index 6a3909d..1ee167f 100644
--- a/benches/scored.rs
+++ b/benches/scored.rs
@@ -9,7 +9,7 @@ fn bench_scored_history(c: &mut Criterion) {
                 .mu(25.0)
                 .sigma(25.0 / 3.0)
                 .beta(25.0 / 6.0)
-                .drift(ConstantDrift(0.03))
+                .drift(ConstantDrift::new(0.03))
                 .score_sigma(2.0)
                 .build();
 
diff --git a/examples/atp.rs b/examples/atp.rs
index 2a967d8..e7bd5a8 100644
--- a/examples/atp.rs
+++ b/examples/atp.rs
@@ -44,7 +44,7 @@ fn main() {
 
     let mut hist: History<i64, _, _, String> = History::builder_with_key()
         .sigma(1.6)
-        .drift(ConstantDrift(0.036))
+        .drift(ConstantDrift::new(0.036))
         .convergence(trueskill_tt::ConvergenceOptions {
             // This history needs 30 sweeps to reach the epsilon below. It was
             // capped at 10 until the `#[must_use]` on `ConvergenceReport`
diff --git a/examples/scored.rs b/examples/scored.rs
index 5a63f81..3566306 100644
--- a/examples/scored.rs
+++ b/examples/scored.rs
@@ -14,7 +14,7 @@ fn main() {
         .mu(25.0)
         .sigma(25.0 / 3.0)
         .beta(25.0 / 6.0)
-        .drift(ConstantDrift(0.03))
+        .drift(ConstantDrift::new(0.03))
         .score_sigma(2.0) // tune to data; smaller = trust margins more
         .build();
 
diff --git a/src/acquisition.rs b/src/acquisition.rs
index 76a236f..23d1eea 100644
--- a/src/acquisition.rs
+++ b/src/acquisition.rs
@@ -208,7 +208,11 @@ mod tests {
     type R = Rating<i64, ConstantDrift>;
 
     fn rating(mu: f64, sigma: f64) -> R {
-        R::new(Gaussian::from_ms(mu, sigma), BETA, ConstantDrift(GAMMA))
+        R::new(
+            Gaussian::from_ms(mu, sigma),
+            BETA,
+            ConstantDrift::new(GAMMA),
+        )
     }
 
     fn options(p_draw: f64) -> GameOptions {
diff --git a/src/drift.rs b/src/drift.rs
index 8f89415..ba36486 100644
--- a/src/drift.rs
+++ b/src/drift.rs
@@ -22,24 +22,57 @@ pub trait Drift<T: Time>: Copy + Debug + Send + Sync {
 /// For `Time = i64`: variance added is `(to - from) * gamma^2`.
 /// For `Time = Untimed`: elapsed is always 0, so drift is always 0.
 ///
-/// # The sign of `gamma` is not meaningful
+/// # Why the field is private
 ///
-/// `gamma` enters only as `gamma * gamma`, so `ConstantDrift(-0.05)` produces
-/// results **bit identical** to `ConstantDrift(0.05)`. That is the same
-/// sign-absorption `HistoryBuilder::sigma`, `HistoryBuilder::beta`,
-/// `Gaussian::from_ms` and `Rating::new` all reject outright.
+/// `gamma` enters only as `gamma * gamma`, so a negative value is squared away:
+/// measured against the old public-field form, `ConstantDrift(-0.0833)` produced
+/// results **bit identical** to `ConstantDrift(0.0833)`. The sign was neither
+/// rejected nor honoured — it vanished. That is the same sign-absorption `HistoryBuilder::sigma`,
+/// `HistoryBuilder::beta`, `Gaussian::from_ms` and `Rating::new` all reject.
 ///
-/// It is not rejected here because the field is public and positional, so
-/// there is no constructor to intercept — sealing it would break every
-/// `ConstantDrift(x)` in existence for a case whose *resulting model* is
-/// perfectly valid, just not the one a caller writing a minus sign expected.
+/// It could not be checked while the field was a public tuple position, because
+/// there was no constructor to intercept. Validating inside
+/// `variance_for_elapsed` would have been worse: it runs inside the sweep, so a
+/// construction-time mistake would panic mid-inference — and `Gaussian::from_ms`
+/// is a worked example of why that is the wrong place for a guard, where
+/// rejecting NaN turned the `NonFiniteResult` reporting path into a crash.
 ///
-/// A non-finite `gamma` is a different matter and **is** rejected:
+/// So [`ConstantDrift::new`] is the only way in, and it checks. Read the value
+/// back with [`ConstantDrift::gamma`].
+///
+/// A non-finite gamma is caught a second time regardless:
 /// `History::converge` validates the drift variance each competitor actually
-/// accumulates, which also covers a custom [`Drift`] implementation, and
-/// reports `InferenceError::InvalidParameter`.
+/// accumulates, which also covers a custom [`Drift`] implementation.
 #[derive(Clone, Copy, Debug)]
-pub struct ConstantDrift(pub f64);
+pub struct ConstantDrift(f64);
+
+impl ConstantDrift {
+    /// Drift of `gamma` standard deviations per unit time.
+    ///
+    /// # Panics
+    ///
+    /// Panics unless `gamma` is finite and non-negative.
+    ///
+    /// The field is private and this is the only constructor precisely so that
+    /// there is somewhere to check. While it was a public tuple field there was
+    /// nothing to intercept, and a negative gamma was silently squared away —
+    /// see the type docs.
+    #[must_use]
+    pub fn new(gamma: f64) -> Self {
+        assert!(
+            gamma.is_finite() && gamma >= 0.0,
+            "gamma must be finite and non-negative (got {gamma}); it is only ever \
+             squared, so a negative value would silently behave as its absolute value"
+        );
+        Self(gamma)
+    }
+
+    /// Standard deviations of drift accumulated per unit time.
+    #[must_use]
+    pub fn gamma(&self) -> f64 {
+        self.0
+    }
+}
 
 impl<T: Time> Drift<T> for ConstantDrift {
     fn variance_delta(&self, from: &T, to: &T) -> f64 {
diff --git a/src/event.rs b/src/event.rs
index 341dd54..f547cc3 100644
--- a/src/event.rs
+++ b/src/event.rs
@@ -99,8 +99,8 @@ impl<K> Member<K> {
     /// Scale how fast this competitor drifts, relative to the history's drift.
     ///
     /// The scale multiplies the drift *variance*, so it is in the same units as
-    /// `gamma`: `ConstantDrift(g)` at `scale = s` behaves exactly as
-    /// `ConstantDrift(g * s)` would for this competitor alone.
+    /// `gamma`: `ConstantDrift::new(g)` at `scale = s` behaves exactly as
+    /// `ConstantDrift::new(g * s)` would for this competitor alone.
     ///
     /// `0.0` pins the competitor still — useful for a reference point that
     /// shares a scale with moving competitors but should not itself move: a bot
diff --git a/src/game.rs b/src/game.rs
index 0977a48..8c97fed 100644
--- a/src/game.rs
+++ b/src/game.rs
@@ -623,12 +623,12 @@ mod tests {
         let t_a = R::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            ConstantDrift(25.0 / 300.0),
+            ConstantDrift::new(25.0 / 300.0),
         );
         let t_b = R::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            ConstantDrift(25.0 / 300.0),
+            ConstantDrift::new(25.0 / 300.0),
         );
 
         let w = [vec![1.0], vec![1.0]];
@@ -651,12 +651,12 @@ mod tests {
         let t_a = R::new(
             Gaussian::from_ms(29.0, 1.0),
             25.0 / 6.0,
-            ConstantDrift(GAMMA),
+            ConstantDrift::new(GAMMA),
         );
         let t_b = R::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            ConstantDrift(GAMMA),
+            ConstantDrift::new(GAMMA),
         );
 
         let w = [vec![1.0], vec![1.0]];
@@ -676,8 +676,16 @@ mod tests {
         assert_ulps_eq!(a, Gaussian::from_ms(28.896475, 0.996604), epsilon = 1e-6);
         assert_ulps_eq!(b, Gaussian::from_ms(32.189211, 6.062063), epsilon = 1e-6);
 
-        let t_a = R::new(Gaussian::from_ms(1.139, 0.531), 1.0, ConstantDrift(0.2125));
-        let t_b = R::new(Gaussian::from_ms(15.568, 0.51), 1.0, ConstantDrift(0.2125));
+        let t_a = R::new(
+            Gaussian::from_ms(1.139, 0.531),
+            1.0,
+            ConstantDrift::new(0.2125),
+        );
+        let t_b = R::new(
+            Gaussian::from_ms(15.568, 0.51),
+            1.0,
+            ConstantDrift::new(0.2125),
+        );
 
         let w = [vec![1.0], vec![1.0]];
         let g = Game::ranked_with_arena(
@@ -699,17 +707,17 @@ mod tests {
             vec![R::new(
                 Gaussian::from_ms(25.0, 25.0 / 3.0),
                 25.0 / 6.0,
-                ConstantDrift(25.0 / 300.0),
+                ConstantDrift::new(25.0 / 300.0),
             )],
             vec![R::new(
                 Gaussian::from_ms(25.0, 25.0 / 3.0),
                 25.0 / 6.0,
-                ConstantDrift(25.0 / 300.0),
+                ConstantDrift::new(25.0 / 300.0),
             )],
             vec![R::new(
                 Gaussian::from_ms(25.0, 25.0 / 3.0),
                 25.0 / 6.0,
-                ConstantDrift(25.0 / 300.0),
+                ConstantDrift::new(25.0 / 300.0),
             )],
         ];
 
@@ -779,12 +787,12 @@ mod tests {
         let t_a = R::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            ConstantDrift(25.0 / 300.0),
+            ConstantDrift::new(25.0 / 300.0),
         );
         let t_b = R::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            ConstantDrift(25.0 / 300.0),
+            ConstantDrift::new(25.0 / 300.0),
         );
 
         let w = [vec![1.0], vec![1.0]];
@@ -811,12 +819,12 @@ mod tests {
         let t_a = R::new(
             Gaussian::from_ms(25.0, 3.0),
             25.0 / 6.0,
-            ConstantDrift(25.0 / 300.0),
+            ConstantDrift::new(25.0 / 300.0),
         );
         let t_b = R::new(
             Gaussian::from_ms(29.0, 2.0),
             25.0 / 6.0,
-            ConstantDrift(25.0 / 300.0),
+            ConstantDrift::new(25.0 / 300.0),
         );
 
         let w = [vec![1.0], vec![1.0]];
@@ -842,17 +850,17 @@ mod tests {
         let t_a = R::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            ConstantDrift(25.0 / 300.0),
+            ConstantDrift::new(25.0 / 300.0),
         );
         let t_b = R::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            ConstantDrift(25.0 / 300.0),
+            ConstantDrift::new(25.0 / 300.0),
         );
         let t_c = R::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            ConstantDrift(25.0 / 300.0),
+            ConstantDrift::new(25.0 / 300.0),
         );
 
         let w = [vec![1.0], vec![1.0], vec![1.0]];
@@ -879,17 +887,17 @@ mod tests {
         let t_a = R::new(
             Gaussian::from_ms(25.0, 3.0),
             25.0 / 6.0,
-            ConstantDrift(25.0 / 300.0),
+            ConstantDrift::new(25.0 / 300.0),
         );
         let t_b = R::new(
             Gaussian::from_ms(25.0, 3.0),
             25.0 / 6.0,
-            ConstantDrift(25.0 / 300.0),
+            ConstantDrift::new(25.0 / 300.0),
         );
         let t_c = R::new(
             Gaussian::from_ms(29.0, 2.0),
             25.0 / 6.0,
-            ConstantDrift(25.0 / 300.0),
+            ConstantDrift::new(25.0 / 300.0),
         );
 
         let w = [vec![1.0], vec![1.0], vec![1.0]];
@@ -918,29 +926,29 @@ mod tests {
             R::new(
                 Gaussian::from_ms(12.0, 3.0),
                 25.0 / 6.0,
-                ConstantDrift(25.0 / 300.0),
+                ConstantDrift::new(25.0 / 300.0),
             ),
             R::new(
                 Gaussian::from_ms(18.0, 3.0),
                 25.0 / 6.0,
-                ConstantDrift(25.0 / 300.0),
+                ConstantDrift::new(25.0 / 300.0),
             ),
         ];
         let t_b = vec![R::new(
             Gaussian::from_ms(30.0, 3.0),
             25.0 / 6.0,
-            ConstantDrift(25.0 / 300.0),
+            ConstantDrift::new(25.0 / 300.0),
         )];
         let t_c = vec![
             R::new(
                 Gaussian::from_ms(14.0, 3.0),
                 25.0 / 6.0,
-                ConstantDrift(25.0 / 300.0),
+                ConstantDrift::new(25.0 / 300.0),
             ),
             R::new(
                 Gaussian::from_ms(16., 3.0),
                 25.0 / 6.0,
-                ConstantDrift(25.0 / 300.0),
+                ConstantDrift::new(25.0 / 300.0),
             ),
         ];
 
@@ -970,12 +978,12 @@ mod tests {
         let t_a = vec![R::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            ConstantDrift(0.0),
+            ConstantDrift::new(0.0),
         )];
         let t_b = vec![R::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            ConstantDrift(0.0),
+            ConstantDrift::new(0.0),
         )];
 
         let w = [w_a, w_b];
@@ -1053,8 +1061,16 @@ mod tests {
         let w_a = vec![1.0];
         let w_b = vec![0.0];
 
-        let t_a = vec![R::new(Gaussian::from_ms(2.0, 6.0), 1.0, ConstantDrift(0.0))];
-        let t_b = vec![R::new(Gaussian::from_ms(2.0, 6.0), 1.0, ConstantDrift(0.0))];
+        let t_a = vec![R::new(
+            Gaussian::from_ms(2.0, 6.0),
+            1.0,
+            ConstantDrift::new(0.0),
+        )];
+        let t_b = vec![R::new(
+            Gaussian::from_ms(2.0, 6.0),
+            1.0,
+            ConstantDrift::new(0.0),
+        )];
 
         let w = [w_a, w_b];
         let g = Game::ranked_with_arena(
@@ -1081,8 +1097,16 @@ mod tests {
         let w_a = vec![1.0];
         let w_b = vec![-1.0];
 
-        let t_a = vec![R::new(Gaussian::from_ms(2.0, 6.0), 1.0, ConstantDrift(0.0))];
-        let t_b = vec![R::new(Gaussian::from_ms(2.0, 6.0), 1.0, ConstantDrift(0.0))];
+        let t_a = vec![R::new(
+            Gaussian::from_ms(2.0, 6.0),
+            1.0,
+            ConstantDrift::new(0.0),
+        )];
+        let t_b = vec![R::new(
+            Gaussian::from_ms(2.0, 6.0),
+            1.0,
+            ConstantDrift::new(0.0),
+        )];
 
         let w = [w_a, w_b];
         let g = Game::ranked_with_arena(
@@ -1125,7 +1149,7 @@ mod tests {
         let prior = R::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            ConstantDrift(25.0 / 300.0),
+            ConstantDrift::new(25.0 / 300.0),
         );
         let teams = vec![vec![prior], vec![prior]];
         let result = vec![10.0, 0.0]; // a beat b by 10
@@ -1175,7 +1199,7 @@ mod tests {
         let prior = R::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            ConstantDrift(25.0 / 300.0),
+            ConstantDrift::new(25.0 / 300.0),
         );
         let opts = GameOptions {
             score_sigma: 1.0,
@@ -1191,7 +1215,7 @@ mod tests {
         let prior = R::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            ConstantDrift(25.0 / 300.0),
+            ConstantDrift::new(25.0 / 300.0),
         );
         let err = Game::scored(
             &[&[prior], &[prior]],
@@ -1210,7 +1234,7 @@ mod tests {
         let prior = R::new(
             Gaussian::from_ms(25.0, 25.0 / 3.0),
             25.0 / 6.0,
-            ConstantDrift(25.0 / 300.0),
+            ConstantDrift::new(25.0 / 300.0),
         );
         let opts = GameOptions {
             score_sigma: 0.0,
@@ -1237,12 +1261,12 @@ mod tests {
             R::new(
                 Gaussian::from_ms(25.0, 25.0 / 3.0),
                 25.0 / 6.0,
-                ConstantDrift(0.0),
+                ConstantDrift::new(0.0),
             ),
             R::new(
                 Gaussian::from_ms(25.0, 25.0 / 3.0),
                 25.0 / 6.0,
-                ConstantDrift(0.0),
+                ConstantDrift::new(0.0),
             ),
         ];
         let w_a = vec![0.4, 0.8];
@@ -1251,12 +1275,12 @@ mod tests {
             R::new(
                 Gaussian::from_ms(25.0, 25.0 / 3.0),
                 25.0 / 6.0,
-                ConstantDrift(0.0),
+                ConstantDrift::new(0.0),
             ),
             R::new(
                 Gaussian::from_ms(25.0, 25.0 / 3.0),
                 25.0 / 6.0,
-                ConstantDrift(0.0),
+                ConstantDrift::new(0.0),
             ),
         ];
         let w_b = vec![0.9, 0.6];
@@ -1370,7 +1394,7 @@ mod tests {
                 vec![R::new(
                     Gaussian::from_ms(25.0, 25.0 / 3.0),
                     25.0 / 6.0,
-                    ConstantDrift(0.0),
+                    ConstantDrift::new(0.0),
                 )],
             ],
             &[1.0, 0.0],
diff --git a/src/history.rs b/src/history.rs
index 5612cf5..bfcae49 100644
--- a/src/history.rs
+++ b/src/history.rs
@@ -139,8 +139,8 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> HistoryBuilder<
     /// Panics if `score_sigma` is not strictly positive.
     pub fn score_sigma(mut self, score_sigma: f64) -> Self {
         assert!(
-            score_sigma > 0.0,
-            "score_sigma must be positive (got {score_sigma})"
+            score_sigma.is_finite() && score_sigma > 0.0,
+            "score_sigma must be finite and positive (got {score_sigma})"
         );
         self.score_sigma = score_sigma;
         self
@@ -224,7 +224,7 @@ impl Default for HistoryBuilder<i64, ConstantDrift, NullObserver, &'static str>
             mu: MU,
             sigma: SIGMA,
             beta: BETA,
-            drift: ConstantDrift(GAMMA),
+            drift: ConstantDrift::new(GAMMA),
             p_draw: P_DRAW,
             score_sigma: 1.0,
             convergence: ConvergenceOptions::default(),
@@ -358,7 +358,7 @@ impl<K: Eq + Hash + Clone> History<i64, ConstantDrift, NullObserver, K> {
             mu: MU,
             sigma: SIGMA,
             beta: BETA,
-            drift: ConstantDrift(GAMMA),
+            drift: ConstantDrift::new(GAMMA),
             p_draw: P_DRAW,
             score_sigma: 1.0,
             convergence: ConvergenceOptions::default(),
@@ -1663,7 +1663,7 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
         // instead, which also covers a custom impl.
         //
         // `ConstantDrift` returns `elapsed * gamma * gamma`, so a negative
-        // gamma is squared away: measured, `ConstantDrift(-0.0833)` gave
+        // gamma is squared away: measured, `ConstantDrift::new(-0.0833)` gave
         // results **bit identical** to `+0.0833`, the same sign-absorption
         // defect already rejected for `sigma` and `beta`. A non-finite gamma
         // poisons every posterior derived from it.
@@ -2606,7 +2606,7 @@ mod tests {
             .mu(25.0)
             .sigma(25.0 / 3.0)
             .beta(25.0 / 6.0)
-            .drift(ConstantDrift(0.15 * 25.0 / 3.0))
+            .drift(ConstantDrift::new(0.15 * 25.0 / 3.0))
             .build();
 
         let events = make_events_1v1(
@@ -2671,7 +2671,7 @@ mod tests {
             .mu(25.0)
             .sigma(25.0 / 3.0)
             .beta(25.0 / 6.0)
-            .drift(ConstantDrift(0.15 * 25.0 / 3.0))
+            .drift(ConstantDrift::new(0.15 * 25.0 / 3.0))
             .build();
 
         let events = make_events_1v1(
@@ -2716,7 +2716,7 @@ mod tests {
             .mu(25.0)
             .sigma(25.0 / 3.0)
             .beta(25.0 / 6.0)
-            .drift(ConstantDrift(25.0 / 300.0))
+            .drift(ConstantDrift::new(25.0 / 300.0))
             .build();
 
         let events = make_events_1v1(
@@ -2764,7 +2764,7 @@ mod tests {
             .mu(25.0)
             .sigma(25.0 / 3.0)
             .beta(25.0 / 6.0)
-            .drift(ConstantDrift(25.0 / 300.0))
+            .drift(ConstantDrift::new(25.0 / 300.0))
             .build();
 
         let events = make_events_1v1(
@@ -2806,7 +2806,7 @@ mod tests {
             .mu(25.0)
             .sigma(25.0 / 3.0)
             .beta(25.0 / 6.0)
-            .drift(ConstantDrift(25.0 / 300.0))
+            .drift(ConstantDrift::new(25.0 / 300.0))
             .build();
 
         let events = make_events_1v1(
@@ -2851,7 +2851,7 @@ mod tests {
             .mu(0.0)
             .sigma(6.0)
             .beta(1.0)
-            .drift(ConstantDrift(0.0))
+            .drift(ConstantDrift::new(0.0))
             .build();
 
         let events: Vec<Event<i64, &'static str>> = vec![
@@ -2957,7 +2957,7 @@ mod tests {
             .mu(0.0)
             .sigma(2.0)
             .beta(1.0)
-            .drift(ConstantDrift(0.0))
+            .drift(ConstantDrift::new(0.0))
             .build();
 
         let events = make_events_1v1(
@@ -3054,7 +3054,7 @@ mod tests {
             .mu(0.0)
             .sigma(2.0)
             .beta(1.0)
-            .drift(ConstantDrift(0.0))
+            .drift(ConstantDrift::new(0.0))
             .build();
 
         let events = make_events_1v1(
@@ -3227,7 +3227,7 @@ mod tests {
             .mu(0.0)
             .sigma(2.0)
             .beta(1.0)
-            .drift(ConstantDrift(0.0))
+            .drift(ConstantDrift::new(0.0))
             .build();
 
         let events = make_events_1v1(
@@ -3330,7 +3330,7 @@ mod tests {
             .mu(0.0)
             .sigma(2.0)
             .beta(1.0)
-            .drift(ConstantDrift(0.0))
+            .drift(ConstantDrift::new(0.0))
             .build();
 
         let events = make_events_1v1(
@@ -3434,7 +3434,7 @@ mod tests {
             .mu(2.0)
             .sigma(6.0)
             .beta(1.0)
-            .drift(ConstantDrift(0.0))
+            .drift(ConstantDrift::new(0.0))
             .build();
 
         // empty results in old API = team 0 wins: a wins event 1, b wins event 2
@@ -3501,7 +3501,7 @@ mod tests {
             .mu(0.0)
             .sigma(2.0)
             .beta(1.0)
-            .drift(ConstantDrift(0.0))
+            .drift(ConstantDrift::new(0.0))
             .convergence(ConvergenceOptions {
                 max_iter: 30,
                 epsilon: 1e-6,
@@ -3528,7 +3528,7 @@ mod tests {
     }
 
     #[test]
-    #[should_panic(expected = "score_sigma must be positive")]
+    #[should_panic(expected = "score_sigma must be finite and positive")]
     fn history_builder_rejects_zero_score_sigma() {
         let _ = History::builder().score_sigma(0.0).build();
     }
diff --git a/src/rating.rs b/src/rating.rs
index 5de6b5c..a58fabc 100644
--- a/src/rating.rs
+++ b/src/rating.rs
@@ -110,7 +110,7 @@ impl Default for Rating<i64, ConstantDrift> {
         Self {
             prior: Gaussian::default(),
             beta: BETA,
-            drift: ConstantDrift(GAMMA),
+            drift: ConstantDrift::new(GAMMA),
             drift_scale: 1.0,
             _time: PhantomData,
         }
diff --git a/src/time_slice.rs b/src/time_slice.rs
index 30b23be..b00fd11 100644
--- a/src/time_slice.rs
+++ b/src/time_slice.rs
@@ -911,7 +911,7 @@ mod tests {
                     rating: Rating::new(
                         Gaussian::from_ms(25.0, 25.0 / 3.0),
                         25.0 / 6.0,
-                        ConstantDrift(25.0 / 300.0),
+                        ConstantDrift::new(25.0 / 300.0),
                     ),
                     ..Default::default()
                 },
@@ -988,7 +988,7 @@ mod tests {
                     rating: Rating::new(
                         Gaussian::from_ms(25.0, 25.0 / 3.0),
                         25.0 / 6.0,
-                        ConstantDrift(25.0 / 300.0),
+                        ConstantDrift::new(25.0 / 300.0),
                     ),
                     ..Default::default()
                 },
@@ -1068,7 +1068,7 @@ mod tests {
                     rating: Rating::new(
                         Gaussian::from_ms(25.0, 25.0 / 3.0),
                         25.0 / 6.0,
-                        ConstantDrift(25.0 / 300.0),
+                        ConstantDrift::new(25.0 / 300.0),
                     ),
                     ..Default::default()
                 },
@@ -1171,7 +1171,7 @@ mod tests {
                     rating: Rating::new(
                         Gaussian::from_ms(25.0, 25.0 / 3.0),
                         25.0 / 6.0,
-                        ConstantDrift(25.0 / 300.0),
+                        ConstantDrift::new(25.0 / 300.0),
                     ),
                     ..Default::default()
                 },
diff --git a/tests/additive_model.rs b/tests/additive_model.rs
index 9738d3c..fbe0c8e 100644
--- a/tests/additive_model.rs
+++ b/tests/additive_model.rs
@@ -34,7 +34,7 @@ fn additive_structure_makes_sums_wide_and_differences_tight() {
         .sigma(6.0)
         .beta(1.0)
         .score_sigma(2.0)
-        .drift(ConstantDrift(0.0))
+        .drift(ConstantDrift::new(0.0))
         .convergence(ConvergenceOptions {
             max_iter: 20_000,
             epsilon: 1e-12,
diff --git a/tests/api_shape.rs b/tests/api_shape.rs
index 6a56e0d..31656d5 100644
--- a/tests/api_shape.rs
+++ b/tests/api_shape.rs
@@ -11,7 +11,7 @@ fn add_events_bulk_via_iter() {
         .sigma(2.0)
         .beta(1.0)
         .p_draw(0.0)
-        .drift(ConstantDrift(0.0))
+        .drift(ConstantDrift::new(0.0))
         .convergence(ConvergenceOptions {
             max_iter: 30,
             epsilon: 1e-6,
@@ -53,7 +53,7 @@ fn add_events_draw() {
         .sigma(25.0 / 3.0)
         .beta(25.0 / 6.0)
         .p_draw(0.25)
-        .drift(ConstantDrift(25.0 / 300.0))
+        .drift(ConstantDrift::new(25.0 / 300.0))
         .build();
 
     let events: Vec<Event<i64, &'static str>> = vec![Event {
@@ -181,7 +181,7 @@ fn log_evidence_total_vs_subset() {
         .sigma(6.0)
         .beta(1.0)
         .p_draw(0.0)
-        .drift(ConstantDrift(0.0))
+        .drift(ConstantDrift::new(0.0))
         .build();
     h.record_winner(&"a", &"b", 1).unwrap();
     h.record_winner(&"b", &"a", 2).unwrap();
@@ -236,7 +236,7 @@ fn fluent_event_builder_scores() {
         .mu(25.0)
         .sigma(25.0 / 3.0)
         .beta(25.0 / 6.0)
-        .drift(ConstantDrift(0.0))
+        .drift(ConstantDrift::new(0.0))
         .build();
 
     h.event(1)
diff --git a/tests/constructor_validation.rs b/tests/constructor_validation.rs
new file mode 100644
index 0000000..9a0574e
--- /dev/null
+++ b/tests/constructor_validation.rs
@@ -0,0 +1,232 @@
+//! Every public entry point that takes a magnitude, in one place.
+//!
+//! This defect class was closed three times in one session and reopened twice,
+//! because each fix validated the layer it had just touched and inferred the
+//! rest: `HistoryBuilder` first, then `Game`'s own entry points, then the
+//! constructors beneath both. A per-site fix cannot notice the site nobody
+//! thought of.
+//!
+//! So this enumerates them. `sigma`, `beta` and `gamma` all enter inference
+//! only as squares, which means a negative value does not fail — it behaves as
+//! its absolute value, bit for bit, and the sign vanishes with no diagnostic.
+//! Non-finite values poison every posterior derived from them.
+//!
+//! Adding a public constructor that takes one of these and not adding it here
+//! is the failure this file exists to make harder.
+
+use std::panic::{AssertUnwindSafe, catch_unwind};
+
+use trueskill_tt::{ConstantDrift, Gaussian, History, Member, Outcome, Rating};
+
+/// Did the entry point refuse the value, by panic or by `Err`?
+fn refuses(f: impl FnOnce() -> bool) -> bool {
+    catch_unwind(AssertUnwindSafe(f)).unwrap_or(true)
+}
+
+/// One entry point, as a name and a closure that applies a value to it.
+type Case = (&'static str, Box<dyn Fn(f64) -> bool>);
+
+/// Entry points that must reject a negative magnitude.
+///
+/// Each closure returns `true` if it refused by returning an error; a panic is
+/// also a refusal and is caught.
+#[test]
+fn every_magnitude_parameter_rejects_a_negative_value() {
+    let cases: Vec<Case> = vec![
+        (
+            "Gaussian::from_ms(sigma)",
+            Box::new(|v| {
+                let _ = Gaussian::from_ms(25.0, v);
+                false
+            }),
+        ),
+        (
+            "Rating::new(beta)",
+            Box::new(|v| {
+                let _ = Rating::<i64, ConstantDrift>::new(
+                    Gaussian::default(),
+                    v,
+                    ConstantDrift::new(0.0),
+                );
+                false
+            }),
+        ),
+        (
+            "ConstantDrift::new(gamma)",
+            Box::new(|v| {
+                let _ = ConstantDrift::new(v);
+                false
+            }),
+        ),
+        (
+            "HistoryBuilder::sigma",
+            Box::new(|v| {
+                let _ = History::builder().sigma(v);
+                false
+            }),
+        ),
+        (
+            "HistoryBuilder::beta",
+            Box::new(|v| {
+                let _ = History::builder().beta(v);
+                false
+            }),
+        ),
+        (
+            "HistoryBuilder::score_sigma",
+            Box::new(|v| {
+                let _ = History::builder().score_sigma(v);
+                false
+            }),
+        ),
+        (
+            "HistoryBuilder::p_draw",
+            Box::new(|v| {
+                let _ = History::builder().p_draw(v);
+                false
+            }),
+        ),
+        (
+            "Member::with_drift_scale (at ingestion)",
+            Box::new(|v| {
+                let mut h = History::builder().build();
+                h.add_events(vec![trueskill_tt::Event {
+                    time: 1i64,
+                    teams: smallvec::smallvec![
+                        trueskill_tt::Team::with_members([Member::new("a").with_drift_scale(v)]),
+                        trueskill_tt::Team::with_members([Member::new("b")]),
+                    ],
+                    outcome: Outcome::winner(0, 2),
+                }])
+                .is_err()
+            }),
+        ),
+        (
+            "Outcome::scores_with_sigma (at ingestion)",
+            Box::new(|v| {
+                let mut h = History::builder().build();
+                h.add_events(vec![trueskill_tt::Event {
+                    time: 1i64,
+                    teams: smallvec::smallvec![
+                        trueskill_tt::Team::with_members([Member::new("a")]),
+                        trueskill_tt::Team::with_members([Member::new("b")]),
+                    ],
+                    outcome: Outcome::scores_with_sigma([3.0, 1.0], v),
+                }])
+                .is_err()
+            }),
+        ),
+    ];
+
+    let mut accepted = Vec::new();
+    for (name, f) in &cases {
+        if !refuses(|| f(-1.0)) {
+            accepted.push(*name);
+        }
+    }
+
+    assert!(
+        accepted.is_empty(),
+        "these accepted a negative magnitude, which is squared away silently \
+         rather than honoured or refused:\n  {}",
+        accepted.join("\n  ")
+    );
+}
+
+/// Same set, for NaN and infinity.
+///
+/// `Gaussian::from_ms` is deliberately absent: a broken fit produces a NaN
+/// sigma legitimately and `converge` reports it as `NonFiniteResult`. Rejecting
+/// it in the constructor turned that reporting path into a panic inside
+/// inference — see the comment on `from_ms`.
+#[test]
+fn every_magnitude_parameter_rejects_a_non_finite_value() {
+    let cases: Vec<Case> = vec![
+        (
+            "Rating::new(beta)",
+            Box::new(|v| {
+                let _ = Rating::<i64, ConstantDrift>::new(
+                    Gaussian::default(),
+                    v,
+                    ConstantDrift::new(0.0),
+                );
+                false
+            }),
+        ),
+        (
+            "ConstantDrift::new(gamma)",
+            Box::new(|v| {
+                let _ = ConstantDrift::new(v);
+                false
+            }),
+        ),
+        (
+            "HistoryBuilder::sigma",
+            Box::new(|v| {
+                let _ = History::builder().sigma(v);
+                false
+            }),
+        ),
+        (
+            "HistoryBuilder::beta",
+            Box::new(|v| {
+                let _ = History::builder().beta(v);
+                false
+            }),
+        ),
+        (
+            "HistoryBuilder::mu",
+            Box::new(|v| {
+                let _ = History::builder().mu(v);
+                false
+            }),
+        ),
+        (
+            "HistoryBuilder::score_sigma",
+            Box::new(|v| {
+                let _ = History::builder().score_sigma(v);
+                false
+            }),
+        ),
+        (
+            "HistoryBuilder::p_draw",
+            Box::new(|v| {
+                let _ = History::builder().p_draw(v);
+                false
+            }),
+        ),
+    ];
+
+    let mut accepted = Vec::new();
+    for (name, f) in &cases {
+        for bad in [f64::NAN, f64::INFINITY] {
+            if !refuses(|| f(bad)) {
+                accepted.push(format!("{name} accepted {bad}"));
+            }
+        }
+    }
+
+    assert!(
+        accepted.is_empty(),
+        "these accepted a non-finite magnitude:\n  {}",
+        accepted.join("\n  ")
+    );
+}
+
+/// The suite must not pass by refusing everything.
+#[test]
+fn ordinary_values_are_still_accepted() {
+    let _ = Gaussian::from_ms(25.0, 8.33);
+    let _ = Rating::<i64, ConstantDrift>::new(Gaussian::default(), 4.17, ConstantDrift::new(0.05));
+    let _ = ConstantDrift::new(0.0833);
+    let _ = History::builder()
+        .mu(25.0)
+        .sigma(8.33)
+        .beta(4.17)
+        .score_sigma(1.0)
+        .p_draw(0.1);
+
+    // Zero beta and zero gamma are legitimate, not degenerate.
+    let _ = ConstantDrift::new(0.0);
+    let _ = Rating::<i64, ConstantDrift>::new(Gaussian::default(), 0.0, ConstantDrift::new(0.0));
+}
diff --git a/tests/convergence_strictness.rs b/tests/convergence_strictness.rs
index 7d6027c..fa18893 100644
--- a/tests/convergence_strictness.rs
+++ b/tests/convergence_strictness.rs
@@ -30,7 +30,7 @@ fn capped(max_iter: usize) -> H {
         .sigma(6.0)
         .beta(1.0)
         .score_sigma(2.0)
-        .drift(ConstantDrift(0.5))
+        .drift(ConstantDrift::new(0.5))
         .convergence(ConvergenceOptions {
             max_iter,
             epsilon: 1e-13,
@@ -112,7 +112,7 @@ fn the_default_cap_clears_an_ordinary_history() {
         .sigma(6.0)
         .beta(1.0)
         .score_sigma(2.0)
-        .drift(ConstantDrift(0.05))
+        .drift(ConstantDrift::new(0.05))
         .build();
 
     let mut events = Vec::new();
diff --git a/tests/cross_process_determinism.rs b/tests/cross_process_determinism.rs
index da9b5ed..79cf320 100644
--- a/tests/cross_process_determinism.rs
+++ b/tests/cross_process_determinism.rs
@@ -32,7 +32,7 @@ fn fitted() -> H {
         .sigma(6.0)
         .beta(1.0)
         .score_sigma(2.0)
-        .drift(ConstantDrift(0.05))
+        .drift(ConstantDrift::new(0.05))
         .unknown_keys(UnknownKeys::Prior)
         .convergence(ConvergenceOptions {
             max_iter: 20_000,
diff --git a/tests/degenerate_inputs.rs b/tests/degenerate_inputs.rs
index 01ef560..61f3c94 100644
--- a/tests/degenerate_inputs.rs
+++ b/tests/degenerate_inputs.rs
@@ -17,7 +17,7 @@ fn rating() -> R {
     R::new(
         Gaussian::from_ms(25.0, 25.0 / 3.0),
         25.0 / 6.0,
-        ConstantDrift(25.0 / 300.0),
+        ConstantDrift::new(25.0 / 300.0),
     )
 }
 
@@ -281,8 +281,16 @@ fn log_evidence_survives_a_long_diff_chain() {
 /// `erfc` approximation; the evidence floor keeps `ln` finite.
 #[test]
 fn log_evidence_finite_for_near_certain_outcome() {
-    let overwhelming = R::new(Gaussian::from_ms(5_000.0, 0.5), 1.0, ConstantDrift(0.0));
-    let hopeless = R::new(Gaussian::from_ms(-5_000.0, 0.5), 1.0, ConstantDrift(0.0));
+    let overwhelming = R::new(
+        Gaussian::from_ms(5_000.0, 0.5),
+        1.0,
+        ConstantDrift::new(0.0),
+    );
+    let hopeless = R::new(
+        Gaussian::from_ms(-5_000.0, 0.5),
+        1.0,
+        ConstantDrift::new(0.0),
+    );
     let a = [overwhelming];
     let b = [hopeless];
     let teams: Vec<&[R]> = vec![&a, &b];
diff --git a/tests/determinism.rs b/tests/determinism.rs
index e6c1da5..bd6657c 100644
--- a/tests/determinism.rs
+++ b/tests/determinism.rs
@@ -43,7 +43,7 @@ fn build_and_converge() -> Fingerprint {
         .mu(25.0)
         .sigma(25.0 / 3.0)
         .beta(25.0 / 6.0)
-        .drift(ConstantDrift(25.0 / 300.0))
+        .drift(ConstantDrift::new(25.0 / 300.0))
         .convergence(ConvergenceOptions {
             max_iter: 20_000,
             epsilon: 1e-9,
diff --git a/tests/drift_scale.rs b/tests/drift_scale.rs
index 50d8904..310a687 100644
--- a/tests/drift_scale.rs
+++ b/tests/drift_scale.rs
@@ -2,7 +2,7 @@
 //!
 //! The scale multiplies the *variance* the history's `Drift` contributes for
 //! that competitor, so `scale` is in the same units as `gamma`:
-//! `ConstantDrift(g)` at `scale = s` behaves as `ConstantDrift(g * s)` would.
+//! `ConstantDrift::new(g)` at `scale = s` behaves as `ConstantDrift::new(g * s)` would.
 //! `scale = 0.0` pins a competitor still — an anchor, a rating floor, a course
 //! difficulty — while everyone around them keeps drifting.
 
@@ -53,7 +53,7 @@ fn fit(events: Vec<Event<i64, &'static str>>, gamma: f64) -> Fit {
         .sigma(25.0 / 3.0)
         .beta(25.0 / 6.0)
         .p_draw(0.0)
-        .drift(ConstantDrift(gamma))
+        .drift(ConstantDrift::new(gamma))
         .convergence(CONVERGENCE)
         .build();
 
@@ -160,7 +160,7 @@ fn scale_is_equivalent_to_scaling_gamma() {
             assert_eq!(t_l, t_r);
             assert!(
                 (g_l.mu() - g_r.mu()).abs() < 1e-9 && (g_l.sigma() - g_r.sigma()).abs() < 1e-9,
-                "ConstantDrift(0.3) at scale 0.5 must equal ConstantDrift(0.15) for {key} at \
+                "ConstantDrift::new(0.3) at scale 0.5 must equal ConstantDrift::new(0.15) for {key} at \
                  t={t_l}: ({}, {}) vs ({}, {})",
                 g_l.mu(),
                 g_l.sigma(),
@@ -218,7 +218,7 @@ fn mixed_static_and_drifting_graph_converges() {
         .sigma(25.0 / 3.0)
         .beta(25.0 / 6.0)
         .p_draw(0.0)
-        .drift(ConstantDrift(25.0 / 300.0))
+        .drift(ConstantDrift::new(25.0 / 300.0))
         .convergence(CONVERGENCE)
         .build();
 
@@ -259,7 +259,7 @@ fn mixed_static_and_drifting_graph_converges() {
 
 fn reject(scale: f64) -> InferenceError {
     let mut h = History::builder()
-        .drift(ConstantDrift(25.0 / 300.0))
+        .drift(ConstantDrift::new(25.0 / 300.0))
         .build();
 
     let events: Vec<Event<i64, &'static str>> = vec![Event {
@@ -360,7 +360,7 @@ fn drift_scale_applies_when_set_after_first_appearance() {
         .sigma(25.0 / 3.0)
         .beta(25.0 / 6.0)
         .p_draw(0.0)
-        .drift(ConstantDrift(25.0 / 300.0))
+        .drift(ConstantDrift::new(25.0 / 300.0))
         .convergence(CONVERGENCE)
         .build();
 
diff --git a/tests/equivalence.rs b/tests/equivalence.rs
index cabd076..46db26b 100644
--- a/tests/equivalence.rs
+++ b/tests/equivalence.rs
@@ -12,7 +12,11 @@ use trueskill_tt::{ConstantDrift, Game, GameOptions, Gaussian, Outcome, Rating};
 type R = Rating<i64, ConstantDrift>;
 
 fn ts_rating(mu: f64, sigma: f64, beta: f64, gamma: f64) -> R {
-    R::new(Gaussian::from_ms(mu, sigma), beta, ConstantDrift(gamma))
+    R::new(
+        Gaussian::from_ms(mu, sigma),
+        beta,
+        ConstantDrift::new(gamma),
+    )
 }
 
 #[test]
diff --git a/tests/event_builder_members.rs b/tests/event_builder_members.rs
index eb5ccc8..f182ab0 100644
--- a/tests/event_builder_members.rs
+++ b/tests/event_builder_members.rs
@@ -19,7 +19,7 @@ fn history() -> H {
         .sigma(6.0)
         .beta(1.0)
         .score_sigma(2.0)
-        .drift(ConstantDrift(0.5))
+        .drift(ConstantDrift::new(0.5))
         .convergence(ConvergenceOptions {
             max_iter: 20_000,
             epsilon: 1e-13,
diff --git a/tests/game.rs b/tests/game.rs
index 8f53dac..5330523 100644
--- a/tests/game.rs
+++ b/tests/game.rs
@@ -8,7 +8,7 @@ fn default_rating() -> R {
     R::new(
         Gaussian::from_ms(25.0, 25.0 / 3.0),
         25.0 / 6.0,
-        ConstantDrift(25.0 / 300.0),
+        ConstantDrift::new(25.0 / 300.0),
     )
 }
 
@@ -40,7 +40,7 @@ fn game_one_v_one_shortcut() {
 
 #[test]
 fn game_ranked_rejects_bad_p_draw() {
-    let a = R::new(Gaussian::default(), 1.0, ConstantDrift(0.0));
+    let a = R::new(Gaussian::default(), 1.0, ConstantDrift::new(0.0));
     let err = Game::<i64, _>::ranked(
         &[&[a], &[a]],
         Outcome::winner(0, 2),
@@ -56,7 +56,7 @@ fn game_ranked_rejects_bad_p_draw() {
 
 #[test]
 fn game_ranked_rejects_mismatched_ranks() {
-    let a = R::new(Gaussian::default(), 1.0, ConstantDrift(0.0));
+    let a = R::new(Gaussian::default(), 1.0, ConstantDrift::new(0.0));
     let err = Game::<i64, _>::ranked(
         &[&[a], &[a]],
         Outcome::ranking([0, 1, 2]),
diff --git a/tests/joint_handle.rs b/tests/joint_handle.rs
index 9a72050..5dc5a99 100644
--- a/tests/joint_handle.rs
+++ b/tests/joint_handle.rs
@@ -41,7 +41,7 @@ fn history(unknown: UnknownKeys) -> H {
         .sigma(6.0)
         .beta(1.0)
         .score_sigma(2.0)
-        .drift(ConstantDrift(0.5))
+        .drift(ConstantDrift::new(0.5))
         .unknown_keys(unknown)
         .convergence(ConvergenceOptions {
             max_iter: 20_000,
@@ -158,7 +158,7 @@ fn drift_free_competitors_shrink_the_joint_by_the_slice_count() {
             .sigma(6.0)
             .beta(1.0)
             .score_sigma(2.0)
-            .drift(ConstantDrift(gamma))
+            .drift(ConstantDrift::new(gamma))
             .convergence(ConvergenceOptions {
                 max_iter: 20_000,
                 epsilon: 1e-13,
@@ -197,7 +197,7 @@ fn pinned_competitors_collapse_consecutive_appearances() {
         .sigma(6.0)
         .beta(1.0)
         .score_sigma(2.0)
-        .drift(ConstantDrift(0.0))
+        .drift(ConstantDrift::new(0.0))
         .convergence(ConvergenceOptions {
             max_iter: 20_000,
             epsilon: 1e-13,
@@ -284,7 +284,7 @@ fn a_drift_too_small_to_represent_collapses_rather_than_corrupting() {
             .sigma(6.0)
             .beta(1.0)
             .score_sigma(2.0)
-            .drift(ConstantDrift(0.5))
+            .drift(ConstantDrift::new(0.5))
             .convergence(ConvergenceOptions {
                 max_iter: 20_000,
                 epsilon: 1e-13,
diff --git a/tests/large_history_converges_finite.rs b/tests/large_history_converges_finite.rs
index 30e6d24..50b376b 100644
--- a/tests/large_history_converges_finite.rs
+++ b/tests/large_history_converges_finite.rs
@@ -27,7 +27,7 @@ fn nan_after_fit(players: usize) -> usize {
     let mut h: History<i64, ConstantDrift, NullObserver, String> = History::builder_with_key()
         .beta(1.0)
         .sigma(6.0)
-        .drift(ConstantDrift(0.1))
+        .drift(ConstantDrift::new(0.1))
         .convergence(ConvergenceOptions {
             max_iter: ITERATIONS,
             epsilon: EPSILON,
diff --git a/tests/marginal_calibration.rs b/tests/marginal_calibration.rs
index 7997bbd..bfe8672 100644
--- a/tests/marginal_calibration.rs
+++ b/tests/marginal_calibration.rs
@@ -140,7 +140,7 @@ fn fitted(
         .sigma(SIGMA0)
         .beta(BETA)
         .score_sigma(SCORE_SIGMA)
-        .drift(ConstantDrift(0.0))
+        .drift(ConstantDrift::new(0.0))
         .convergence(ConvergenceOptions {
             max_iter: 20_000,
             epsilon: 1e-13,
@@ -324,7 +324,7 @@ fn cost_scaling() {
         let names: Vec<String> = (0..n).map(|i| format!("c{i}")).collect();
         let mut h: History<i64, _, _, String> = History::builder_with_key()
             .score_sigma(2.0)
-            .drift(ConstantDrift(0.0))
+            .drift(ConstantDrift::new(0.0))
             .convergence(ConvergenceOptions {
                 max_iter: 200,
                 epsilon: 1e-8,
diff --git a/tests/non_finite_results.rs b/tests/non_finite_results.rs
index b7db0f0..26f7424 100644
--- a/tests/non_finite_results.rs
+++ b/tests/non_finite_results.rs
@@ -191,7 +191,7 @@ fn a_narrow_draw_margin_far_into_the_tail_still_fits() {
             .sigma(sd)
             .beta(beta)
             .p_draw(p_draw)
-            .drift(ConstantDrift(0.0))
+            .drift(ConstantDrift::new(0.0))
             .build();
         h.add_events(vec![Event {
             time: 1i64,
diff --git a/tests/predict_margin.rs b/tests/predict_margin.rs
index cd54fb7..95b70c5 100644
--- a/tests/predict_margin.rs
+++ b/tests/predict_margin.rs
@@ -14,7 +14,7 @@ fn builder(
         .sigma(6.0)
         .beta(1.0)
         .score_sigma(2.0)
-        .drift(ConstantDrift(0.0))
+        .drift(ConstantDrift::new(0.0))
         .unknown_keys(policy)
         .convergence(ConvergenceOptions {
             max_iter: 5_000,
diff --git a/tests/prediction_bounds.rs b/tests/prediction_bounds.rs
index eedde48..0b9267e 100644
--- a/tests/prediction_bounds.rs
+++ b/tests/prediction_bounds.rs
@@ -74,8 +74,16 @@ fn information_gain_never_exceeds_the_entropy_of_the_outcome() {
         let sigma_b = rng.log_uniform(1e-4, 1e2);
         let beta = rng.log_uniform(1e-4, 1e1);
 
-        let a = R::new(Gaussian::from_ms(mu_a, sigma_a), beta, ConstantDrift(0.0));
-        let b = R::new(Gaussian::from_ms(mu_b, sigma_b), beta, ConstantDrift(0.0));
+        let a = R::new(
+            Gaussian::from_ms(mu_a, sigma_a),
+            beta,
+            ConstantDrift::new(0.0),
+        );
+        let b = R::new(
+            Gaussian::from_ms(mu_b, sigma_b),
+            beta,
+            ConstantDrift::new(0.0),
+        );
         let options = GameOptions {
             p_draw: 0.0,
             ..GameOptions::default()
@@ -129,12 +137,12 @@ fn the_known_ceiling_violation_no_longer_answers_wrongly() {
     let a = R::new(
         Gaussian::from_ms(9.577_887_112_129_012, 0.000_132_507_526_585_134_38),
         0.000_307_235_559_013_096_2,
-        ConstantDrift(0.0),
+        ConstantDrift::new(0.0),
     );
     let b = R::new(
         Gaussian::from_ms(-14.114_932_828_525_696, 91.586_690_140_921_16),
         0.000_307_235_559_013_096_2,
-        ConstantDrift(0.0),
+        ConstantDrift::new(0.0),
     );
     let options = GameOptions {
         p_draw: 0.0,
diff --git a/tests/record_winner.rs b/tests/record_winner.rs
index d040d62..2e2b84b 100644
--- a/tests/record_winner.rs
+++ b/tests/record_winner.rs
@@ -6,7 +6,7 @@ fn record_winner_builds_history() {
         .mu(25.0)
         .sigma(25.0 / 3.0)
         .beta(25.0 / 6.0)
-        .drift(ConstantDrift(25.0 / 300.0))
+        .drift(ConstantDrift::new(25.0 / 300.0))
         .convergence(ConvergenceOptions {
             max_iter: 30,
             epsilon: 1e-6,
@@ -43,7 +43,7 @@ fn record_draw_with_p_draw_set() {
         .mu(25.0)
         .sigma(25.0 / 3.0)
         .beta(25.0 / 6.0)
-        .drift(ConstantDrift(25.0 / 300.0))
+        .drift(ConstantDrift::new(25.0 / 300.0))
         .p_draw(0.25)
         .build();
 
diff --git a/tests/registration.rs b/tests/registration.rs
index df7dee4..45555ae 100644
--- a/tests/registration.rs
+++ b/tests/registration.rs
@@ -21,7 +21,7 @@ fn history() -> H {
         .sigma(6.0)
         .beta(1.0)
         .score_sigma(2.0)
-        .drift(ConstantDrift(0.5))
+        .drift(ConstantDrift::new(0.5))
         .convergence(ConvergenceOptions {
             max_iter: 20_000,
             epsilon: 1e-13,
diff --git a/tests/scored.rs b/tests/scored.rs
index a1419e3..8623817 100644
--- a/tests/scored.rs
+++ b/tests/scored.rs
@@ -9,7 +9,7 @@ fn scored_two_team_one_event_pulls_winner_up() {
         .mu(0.0)
         .sigma(2.0)
         .beta(1.0)
-        .drift(ConstantDrift(0.0))
+        .drift(ConstantDrift::new(0.0))
         .score_sigma(1.0)
         .build();
 
@@ -46,7 +46,7 @@ fn scored_zero_margin_treats_as_tie() {
         .mu(0.0)
         .sigma(2.0)
         .beta(1.0)
-        .drift(ConstantDrift(0.0))
+        .drift(ConstantDrift::new(0.0))
         .score_sigma(1.0)
         .build();
 
@@ -88,7 +88,7 @@ fn scored_three_team_partial_order() {
         .mu(0.0)
         .sigma(2.0)
         .beta(1.0)
-        .drift(ConstantDrift(0.0))
+        .drift(ConstantDrift::new(0.0))
         .score_sigma(1.0)
         .build();
 
diff --git a/tests/time_expanded_joint.rs b/tests/time_expanded_joint.rs
index 1080a1a..5ace6c1 100644
--- a/tests/time_expanded_joint.rs
+++ b/tests/time_expanded_joint.rs
@@ -24,7 +24,7 @@ fn history(gamma: f64) -> H {
         .sigma(SIGMA0)
         .beta(BETA)
         .score_sigma(SCORE_SIGMA)
-        .drift(ConstantDrift(gamma))
+        .drift(ConstantDrift::new(gamma))
         .unknown_keys(UnknownKeys::Reject)
         .convergence(ConvergenceOptions {
             max_iter: 20_000,
diff --git a/tests/validation.rs b/tests/validation.rs
index a798fdf..cbb5abb 100644
--- a/tests/validation.rs
+++ b/tests/validation.rs
@@ -22,7 +22,7 @@ fn rating() -> R {
     R::new(
         Gaussian::from_ms(25.0, 25.0 / 3.0),
         25.0 / 6.0,
-        ConstantDrift(0.0),
+        ConstantDrift::new(0.0),
     )
 }
 
@@ -286,33 +286,66 @@ mod constructor_parameters {
     #[test]
     #[should_panic(expected = "beta must be finite and non-negative")]
     fn a_negative_beta_is_rejected_by_rating_new() {
-        let _ = Rating::<i64, ConstantDrift>::new(Gaussian::default(), -4.17, ConstantDrift(0.0));
+        let _ =
+            Rating::<i64, ConstantDrift>::new(Gaussian::default(), -4.17, ConstantDrift::new(0.0));
     }
 
     #[test]
     #[should_panic(expected = "beta must be finite and non-negative")]
     fn a_nan_beta_is_rejected_by_rating_new() {
-        let _ =
-            Rating::<i64, ConstantDrift>::new(Gaussian::default(), f64::NAN, ConstantDrift(0.0));
+        let _ = Rating::<i64, ConstantDrift>::new(
+            Gaussian::default(),
+            f64::NAN,
+            ConstantDrift::new(0.0),
+        );
     }
 
     #[test]
     fn a_zero_beta_is_accepted_by_rating_new() {
-        let _ = Rating::<i64, ConstantDrift>::new(Gaussian::default(), 0.0, ConstantDrift(0.0));
+        let _ =
+            Rating::<i64, ConstantDrift>::new(Gaussian::default(), 0.0, ConstantDrift::new(0.0));
+    }
+
+    /// `ConstantDrift` rejects at construction now that its field is private.
+    #[test]
+    #[should_panic(expected = "gamma must be finite and non-negative")]
+    fn a_negative_gamma_is_rejected_by_constant_drift_new() {
+        let _ = ConstantDrift::new(-0.0833);
+    }
+
+    #[test]
+    #[should_panic(expected = "gamma must be finite and non-negative")]
+    fn a_non_finite_gamma_is_rejected_by_constant_drift_new() {
+        let _ = ConstantDrift::new(f64::NAN);
+    }
+
+    #[test]
+    fn gamma_reads_back_what_was_given() {
+        assert_eq!(ConstantDrift::new(0.25).gamma(), 0.25);
+        assert_eq!(ConstantDrift::new(0.0).gamma(), 0.0);
     }
 
     /// `HistoryBuilder::drift` is generic and cannot inspect an arbitrary
-    /// `Drift`, so the check is on the variance each competitor actually
-    /// accumulates. That also covers a custom implementation.
+    /// `Drift`, so the check on the variance each competitor accumulates is
+    /// still needed — it is the only thing standing between a custom
+    /// implementation and a NaN fit. `ConstantDrift` can no longer reach it,
+    /// so this uses an implementation that can.
     #[test]
-    fn a_non_finite_drift_is_rejected_at_convergence() {
-        for gamma in [f64::NAN, f64::INFINITY] {
-            let mut h = History::builder()
-                .mu(25.0)
-                .sigma(25.0 / 3.0)
-                .beta(25.0 / 6.0)
-                .drift(ConstantDrift(gamma))
-                .build();
+    fn a_custom_drift_returning_a_bad_variance_is_rejected_at_convergence() {
+        #[derive(Clone, Copy, Debug)]
+        struct BadDrift(f64);
+
+        impl trueskill_tt::Drift<i64> for BadDrift {
+            fn variance_delta(&self, _from: &i64, _to: &i64) -> f64 {
+                self.0
+            }
+            fn variance_for_elapsed(&self, _elapsed: i64) -> f64 {
+                self.0
+            }
+        }
+
+        for bad in [f64::NAN, f64::INFINITY, -1.0] {
+            let mut h = History::builder().drift(BadDrift(bad)).build();
             h.record_winner(&"a", &"b", 1).unwrap();
             h.record_winner(&"a", &"b", 5).unwrap();
             let err = h.converge().unwrap_err();
@@ -324,7 +357,7 @@ mod constructor_parameters {
                         ..
                     }
                 ),
-                "gamma {gamma}: {err:?}"
+                "drift {bad}: {err:?}"
             );
         }
     }
@@ -333,7 +366,7 @@ mod constructor_parameters {
     #[test]
     fn an_ordinary_drift_still_converges() {
         let mut h = History::builder()
-            .drift(ConstantDrift(25.0 / 300.0))
+            .drift(ConstantDrift::new(25.0 / 300.0))
             .build();
         h.record_winner(&"a", &"b", 1).unwrap();
         h.record_winner(&"a", &"b", 5).unwrap();
diff --git a/tests/variance_reduction.rs b/tests/variance_reduction.rs
index 0255061..c1abcea 100644
--- a/tests/variance_reduction.rs
+++ b/tests/variance_reduction.rs
@@ -35,7 +35,7 @@ fn fit(extra: Option<Event<i64, &'static str>>, policy: UnknownKeys) -> H {
         .sigma(6.0)
         .beta(1.0)
         .score_sigma(2.0)
-        .drift(ConstantDrift(0.0))
+        .drift(ConstantDrift::new(0.0))
         .unknown_keys(policy)
         .convergence(ConvergenceOptions {
             max_iter: 20_000,