diff --git a/packages/cdk-assets/lib/private/archive.ts b/packages/cdk-assets/lib/private/archive.ts
index 36eedbddbf8e8..17137edfc8d58 100644
--- a/packages/cdk-assets/lib/private/archive.ts
+++ b/packages/cdk-assets/lib/private/archive.ts
@@ -11,7 +11,7 @@ type Logger = (x: string) => void;
 export async function zipDirectory(directory: string, outputFile: string, logger: Logger): Promise<void> {
   // We write to a temporary file and rename at the last moment. This is so that if we are
   // interrupted during this process, we don't leave a half-finished file in the target location.
-  const temporaryOutputFile = `${outputFile}.${randomString()}._tmp`;
+  const temporaryOutputFile = `${outputFile}._tmp`;
   await writeZipFile(directory, temporaryOutputFile);
   await moveIntoPlace(temporaryOutputFile, outputFile, logger);
 }
@@ -97,7 +97,3 @@ async function pathExists(x: string) {
     throw e;
   }
 }
-
-function randomString() {
-  return Math.random().toString(36).replace(/[^a-z0-9]+/g, '');
-}
diff --git a/packages/cdk-assets/lib/private/handlers/files.ts b/packages/cdk-assets/lib/private/handlers/files.ts
index da6fbc56c061c..4395ba8e70ef0 100644
--- a/packages/cdk-assets/lib/private/handlers/files.ts
+++ b/packages/cdk-assets/lib/private/handlers/files.ts
@@ -107,7 +107,7 @@ export class FileAssetHandler implements IAssetHandler {
       const contentType = 'application/zip';
 
       await fs.mkdir(this.fileCacheRoot, { recursive: true });
-      const packagedPath = path.join(this.fileCacheRoot, `${this.asset.id.assetId}.zip`);
+      const packagedPath = path.join(this.fileCacheRoot, `${this.asset.id.assetId}.${randomString()}.zip`);
 
       if (await pathExists(packagedPath)) {
         this.host.emitMessage(EventType.CACHED, `From cache ${packagedPath}`);
@@ -272,3 +272,7 @@ async function cached<A, B>(cache: Map<A, B>, key: A, factory: (x: A) => Promise
   cache.set(key, fresh);
   return fresh;
 }
+
+function randomString() {
+  return Math.random().toString(36).replace(/[^a-z0-9]+/g, '');
+}