diff --git a/src/lib.rs b/src/lib.rs
index 87acc34..4bc7738 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -96,14 +96,14 @@ impl BitSet {
     }
 
     pub fn is_subset(&self, other: &BitSet) -> bool {
-        if self.len() > other.len() {
+        if self.nbits > other.nbits {
             false
         } else {
             self.blocks
                 .iter()
                 .all(|(key, block_a)| match other.blocks.get(key) {
                     Some(block_b) => block_a | block_b == *block_b,
-                    None => false,
+                    None => *block_a == 0,
                 })
         }
     }
@@ -145,8 +145,7 @@ impl BitSet {
         }
     }
 
-    #[inline]
-    pub fn extend_from_bitset(&mut self, other: &Self) {
+    pub fn union_with(&mut self, other: &Self) {
         for (key, value) in &other.blocks {
             *self.blocks.entry(*key).or_insert(0) |= value;
         }
@@ -470,6 +469,23 @@ mod tests {
         assert!(!a.is_superset(&b));
         assert!(!b.is_subset(&a));
         assert!(b.is_superset(&a));
+
+        let mut a = BitSet::new();
+        assert!(a.insert(0));
+        assert!(a.insert(5));
+        assert!(a.insert(11));
+        assert!(a.insert(7));
+
+        let mut b = BitSet::new();
+        assert!(b.insert(0));
+        assert!(b.insert(7));
+        assert!(b.insert(250));
+
+        assert!(!b.is_subset(&a));
+
+        b.remove(&250);
+
+        assert!(b.is_subset(&a));
     }
 
     #[test]
@@ -612,11 +628,11 @@ mod tests {
     }
 
     #[test]
-    fn test_extend_from_bitset() {
+    fn test_union_with() {
         let mut set = [1, 2, 3].iter().cloned().collect::<BitSet>();
         let other = [3, 4, 5].iter().cloned().collect::<BitSet>();
 
-        set.extend_from_bitset(&other);
+        set.union_with(&other);
 
         assert_eq!(set.len(), 5);