diff --git a/crates/ty_python_semantic/resources/mdtest/binary/booleans.md b/crates/ty_python_semantic/resources/mdtest/binary/booleans.md
index 6bfca0ecce..e0bcca56e9 100644
--- a/crates/ty_python_semantic/resources/mdtest/binary/booleans.md
+++ b/crates/ty_python_semantic/resources/mdtest/binary/booleans.md
@@ -103,3 +103,65 @@ def _(a: bool):
         reveal_type(x / y)  # revealed: int | float
         reveal_type(x % y)  # revealed: int
 ```
+
+## Bitwise operations with a variable
+
+```py
+import random
+
+def _(a: bool):
+    def lhs_is_int(x: int):
+        reveal_type(x | a)  # revealed: int
+        reveal_type(x & a)  # revealed: int
+        reveal_type(x ^ a)  # revealed: int
+
+    def rhs_is_int(x: int):
+        reveal_type(a | x)  # revealed: int
+        reveal_type(a & x)  # revealed: int
+        reveal_type(a ^ x)  # revealed: int
+
+    def lhs_is_int_literal():
+        reveal_type(0 | a)  # revealed: int
+        reveal_type(0 & a)  # revealed: int
+        reveal_type(0 ^ a)  # revealed: int
+
+        reveal_type(1 | a)  # revealed: int
+        reveal_type(1 & a)  # revealed: int
+        reveal_type(1 ^ a)  # revealed: int
+
+    def lhs_is_true():
+        reveal_type(True | a)  # revealed: bool
+        reveal_type(True & a)  # revealed: bool
+        reveal_type(True ^ a)  # revealed: bool
+
+    def rhs_is_true():
+        reveal_type(a | True)  # revealed: bool
+        reveal_type(a & True)  # revealed: bool
+        reveal_type(a ^ True)  # revealed: bool
+
+    def lhs_is_false():
+        reveal_type(False | a)  # revealed: bool
+        reveal_type(False & a)  # revealed: bool
+        reveal_type(False ^ a)  # revealed: bool
+
+    def rhs_is_false():
+        reveal_type(a | False)  # revealed: bool
+        reveal_type(a & False)  # revealed: bool
+        reveal_type(a ^ False)  # revealed: bool
+
+    def both_are_bool(x: bool, y: bool):
+        reveal_type(x | y)  # revealed: bool
+        reveal_type(x & y)  # revealed: bool
+        reveal_type(x ^ y)  # revealed: bool
+
+    def lhs_is_int_literal_rhs_is_bool_literal():
+        reveal_type(0 & True)  # revealed: Literal[0]
+        reveal_type(0 | True)  # revealed: Literal[1]
+        reveal_type(3 & True)  # revealed: Literal[1]
+        reveal_type(3 | True)  # revealed: Literal[3]
+
+        reveal_type(0 & False)  # revealed: Literal[0]
+        reveal_type(0 | False)  # revealed: Literal[0]
+        reveal_type(3 & False)  # revealed: Literal[0]
+        reveal_type(3 | False)  # revealed: Literal[3]
+```
diff --git a/crates/ty_python_semantic/src/types/infer.rs b/crates/ty_python_semantic/src/types/infer.rs
index b2f941da31..4f7180ee31 100644
--- a/crates/ty_python_semantic/src/types/infer.rs
+++ b/crates/ty_python_semantic/src/types/infer.rs
@@ -6893,22 +6893,22 @@ impl<'db, 'ast> TypeInferenceBuilder<'db, 'ast> {
             (Type::BooleanLiteral(b1), Type::BooleanLiteral(b2), ast::Operator::BitXor) => {
                 Some(Type::BooleanLiteral(b1 ^ b2))
             }
-
-            (Type::BooleanLiteral(bool_value), right, op) => self.infer_binary_expression_type(
-                node,
-                emitted_division_by_zero_diagnostic,
-                Type::IntLiteral(i64::from(bool_value)),
-                right,
-                op,
-            ),
-            (left, Type::BooleanLiteral(bool_value), op) => self.infer_binary_expression_type(
-                node,
-                emitted_division_by_zero_diagnostic,
-                left,
-                Type::IntLiteral(i64::from(bool_value)),
-                op,
-            ),
-
+            (Type::BooleanLiteral(b1), Type::BooleanLiteral(_) | Type::IntLiteral(_), op) => self
+                .infer_binary_expression_type(
+                    node,
+                    emitted_division_by_zero_diagnostic,
+                    Type::IntLiteral(i64::from(b1)),
+                    right_ty,
+                    op,
+                ),
+            (Type::IntLiteral(_), Type::BooleanLiteral(b2), op) => self
+                .infer_binary_expression_type(
+                    node,
+                    emitted_division_by_zero_diagnostic,
+                    left_ty,
+                    Type::IntLiteral(i64::from(b2)),
+                    op,
+                ),
             (Type::Tuple(lhs), Type::Tuple(rhs), ast::Operator::Add) => {
                 // Note: this only works on heterogeneous tuples.
                 let lhs_elements = lhs.elements(self.db());
@@ -6927,6 +6927,7 @@ impl<'db, 'ast> TypeInferenceBuilder<'db, 'ast> {
             // fall back on looking for dunder methods on one of the operand types.
             (
                 Type::FunctionLiteral(_)
+                | Type::BooleanLiteral(_)
                 | Type::Callable(..)
                 | Type::BoundMethod(_)
                 | Type::WrapperDescriptor(_)
@@ -6954,6 +6955,7 @@ impl<'db, 'ast> TypeInferenceBuilder<'db, 'ast> {
                 | Type::TypeVar(_)
                 | Type::TypeIs(_),
                 Type::FunctionLiteral(_)
+                | Type::BooleanLiteral(_)
                 | Type::Callable(..)
                 | Type::BoundMethod(_)
                 | Type::WrapperDescriptor(_)