diff --git a/packages/@aws-cdk/cdk-assets-lib/lib/private/p-limit.ts b/packages/@aws-cdk/cdk-assets-lib/lib/private/p-limit.ts
index fb62e18da..a909baf3a 100644
--- a/packages/@aws-cdk/cdk-assets-lib/lib/private/p-limit.ts
+++ b/packages/@aws-cdk/cdk-assets-lib/lib/private/p-limit.ts
@@ -10,6 +10,9 @@ export function pLimit(concurrency: number): PLimit {
   let stopped = false;
 
   function dispatch() {
+    if (stopped) {
+      return;
+    }
     if (activeCount < concurrency && queue.length > 0) {
       const [fac, resolve, reject] = queue.shift()!;
       activeCount++;
@@ -41,6 +44,10 @@ export function pLimit(concurrency: number): PLimit {
 
   const ret = <A>(promiseFactory: PromiseFactory<A>) => {
     return new Promise<A>((resolve, reject) => {
+      if (stopped) {
+        reject(new Error('Task has been cancelled'));
+        return;
+      }
       queue.push([promiseFactory, resolve, reject]);
       dispatch();
     });
diff --git a/packages/@aws-cdk/cdk-assets-lib/test/private/p-limit.test.ts b/packages/@aws-cdk/cdk-assets-lib/test/private/p-limit.test.ts
index 209e1d691..f4693aaac 100644
--- a/packages/@aws-cdk/cdk-assets-lib/test/private/p-limit.test.ts
+++ b/packages/@aws-cdk/cdk-assets-lib/test/private/p-limit.test.ts
@@ -43,6 +43,23 @@ test('new jobs arent started after dispose is called', async () => {
   expect(started).toBeLessThanOrEqual(3);
 });
 
+test('no new job is started once dispose is called, even with a free slot', async () => {
+  const limit = pLimit(1);
+
+  limit.dispose();
+
+  let ran = false;
+  await expect(
+    limit(async () => {
+      ran = true;
+    }),
+  ).rejects.toThrow(/cancelled/);
+
+  // activeCount was 0 and concurrency is 1, so before the fix dispatch()
+  // would start this job immediately despite dispose() having been called.
+  expect(ran).toBe(false);
+});
+
 function sleep(ms: number) {
   return new Promise((resolve) => setTimeout(resolve, ms));
 }