diff --git a/src/behavior.ts b/src/behavior.ts
index 627832f..d790572 100644
--- a/src/behavior.ts
+++ b/src/behavior.ts
@@ -274,6 +274,18 @@ export class LiftBehavior<A extends any[], R> extends Behavior<R> {
   update(_t: number): R {
     return this.f(...(this.bs.map((b) => b.last) as any));
   }
+  changeStateDown(_: State): void {
+    let state = State.Done;
+    for (const p of this.parents) {
+      state = Math.max(state, p.state);
+    }
+    if (this.state !== state) {
+      this.state = state;
+      for (const child of this.children) {
+        child.changeStateDown(state);
+      }
+    }
+  }
 }
 
 class FlatMapBehavior<A, B> extends Behavior<B> {
diff --git a/test/behavior.ts b/test/behavior.ts
index 61f3e2f..780dfbc 100644
--- a/test/behavior.ts
+++ b/test/behavior.ts
@@ -316,6 +316,31 @@ describe("behavior", () => {
         p.newValue(4);
         assert.deepEqual(cb.args, [[16], [24]]);
       });
+      it("only switched to push if all parents are push", () => {
+        // In this test the lifted behavior `b3` starts out in the pull state
+        // since both of its parents are in pull. Then one of the parents
+        // switches to push. But, since one parent is still in pull the lifted
+        // behavior should remain in pull.
+        let n = 1;
+        const b1 = H.fromFunction(() => n);
+        const fut = H.sinkFuture<H.Behavior<number>>();
+        const b2 = H.switchTo(fromFunction(() => 2), fut);
+        const b3 = H.lift((n, m) => n + m, b1, b2);
+        observe(
+          () => {},
+          () => {
+            return () => {
+              throw new Error("Should not be called.");
+            };
+          },
+          b3
+        );
+        expect(H.at(b3)).toEqual(3);
+        fut.resolve(H.sinkBehavior(5));
+        expect(H.at(b3)).toEqual(6);
+        n = 2;
+        expect(H.at(b3)).toEqual(7);
+      });
     });
   });
   describe("flatMap", () => {