diff --git a/Sources/PropertyBased/Gen+Collection.swift b/Sources/PropertyBased/Gen+Collection.swift
index f339f23..f79f576 100644
--- a/Sources/PropertyBased/Gen+Collection.swift
+++ b/Sources/PropertyBased/Gen+Collection.swift
@@ -226,6 +226,6 @@ extension Gen where Value: OptionSet & Sendable, Value.RawValue: FixedWidthInteg
     /// - Parameter options: The options to choose from.
     /// - Returns: A generator of option sets.
     public static func optionSet(of options: Value) -> Generator<Value, Shrink.Bitwise<Value.RawValue>> {
-        Gen<Value.RawValue>.bitSet.map { Value(rawValue: $0 & options.rawValue) }
+        Gen<Value.RawValue>.bitSet(mask: options.rawValue).map { Value(rawValue: $0) }
     }
 }
diff --git a/Sources/PropertyBased/Gen+Int.swift b/Sources/PropertyBased/Gen+Int.swift
index eae3d31..3e5fac1 100644
--- a/Sources/PropertyBased/Gen+Int.swift
+++ b/Sources/PropertyBased/Gen+Int.swift
@@ -39,9 +39,17 @@ extension Gen where Value: FixedWidthInteger & Sendable {
     ///
     /// The associated shrinker will remove every bit, but will never set bits that are unset in the original value.
     @inlinable
-    public static var bitSet: Generator<Value, Shrink.Bitwise<Value>> {
+    public static var bitSet: Generator<Value, Shrink.Bitwise<Value>> { bitSet() }
+
+    /// Produces a generator of random integers within the given bit mask.
+    ///
+    /// The associated shrinker will remove every bit, but will never set bits that are unset in the original value.
+    /// - Parameter mask: The bit mask to apply to each generated value.
+    /// - Returns: A generator of random values.
+    @inlinable
+    public static func bitSet(mask: Value = ~0) -> Generator<Value, Shrink.Bitwise<Value>> {
         return .init(
-            run: { rng in Value.random(in: .min ... .max, using: &rng) },
+            run: { rng in Value.random(in: .min ... .max, using: &rng) & mask },
             shrink: { .init($0) }
         )
     }