diff --git a/packages/@aws-cdk/core/lib/stack.ts b/packages/@aws-cdk/core/lib/stack.ts
index b56d13d4bf642..7f8e3e9a898c6 100644
--- a/packages/@aws-cdk/core/lib/stack.ts
+++ b/packages/@aws-cdk/core/lib/stack.ts
@@ -1184,12 +1184,11 @@ export class Stack extends Construct implements ITaggable {
    * Indicates whether the stack requires bundling or not
    */
   public get bundlingRequired() {
-    const bundlingStacks: string[] = this.node.tryGetContext(cxapi.BUNDLING_STACKS) ?? ['*'];
+    const bundlingStacks: string[] = this.node.tryGetContext(cxapi.BUNDLING_STACKS) ?? ['**'];
 
-    // bundlingStacks is of the form `Stage/Stack`, convert it to `Stage-Stack` before comparing to stack name
     return bundlingStacks.some(pattern => minimatch(
-      this.stackName,
-      pattern.replace('/', '-'),
+      this.node.path, // use the same value for pattern matching as the aws-cdk CLI (displayName / hierarchicalId)
+      pattern,
     ));
   }
 }
diff --git a/packages/@aws-cdk/core/test/staging.test.ts b/packages/@aws-cdk/core/test/staging.test.ts
index 46f20f4ad03f9..16e14f492adaf 100644
--- a/packages/@aws-cdk/core/test/staging.test.ts
+++ b/packages/@aws-cdk/core/test/staging.test.ts
@@ -930,6 +930,155 @@ describe('staging', () => {
     expect(dockerStubInput).not.toMatch(DockerStubCommand.MULTIPLE_FILES);
   });
 
+  test('correctly skips bundling with stack under stage and custom stack name', () => {
+    // GIVEN
+    const app = new App();
+
+    const stage = new Stage(app, 'Stage');
+    stage.node.setContext(cxapi.BUNDLING_STACKS, ['Stage/Stack1']);
+
+    const stack1 = new Stack(stage, 'Stack1', { stackName: 'unrelated-stack1-name' });
+    const stack2 = new Stack(stage, 'Stack2', { stackName: 'unrelated-stack2-name' });
+    const directory = path.join(__dirname, 'fs', 'fixtures', 'test1');
+
+    // WHEN
+    new AssetStaging(stack1, 'Asset', {
+      sourcePath: directory,
+      assetHashType: AssetHashType.OUTPUT,
+      bundling: {
+        image: DockerImage.fromRegistry('alpine'),
+        command: [DockerStubCommand.SUCCESS],
+      },
+    });
+
+    new AssetStaging(stack2, 'Asset', {
+      sourcePath: directory,
+      assetHashType: AssetHashType.OUTPUT,
+      bundling: {
+        image: DockerImage.fromRegistry('alpine'),
+        command: [DockerStubCommand.MULTIPLE_FILES],
+      },
+    });
+
+    // THEN
+    const dockerStubInput = readDockerStubInputConcat();
+    // Docker ran for the asset in Stack1
+    expect(dockerStubInput).toMatch(DockerStubCommand.SUCCESS);
+    // Docker did not run for the asset in Stack2
+    expect(dockerStubInput).not.toMatch(DockerStubCommand.MULTIPLE_FILES);
+  });
+
+  test('correctly bundles with stack under stage and the default stack pattern', () => {
+    // GIVEN
+    const app = new App();
+
+    const stage = new Stage(app, 'Stage');
+
+    const stack1 = new Stack(stage, 'Stack1');
+    const stack2 = new Stack(stage, 'Stack2');
+    const directory = path.join(__dirname, 'fs', 'fixtures', 'test1');
+
+    // WHEN
+    new AssetStaging(stack1, 'Asset', {
+      sourcePath: directory,
+      assetHashType: AssetHashType.OUTPUT,
+      bundling: {
+        image: DockerImage.fromRegistry('alpine'),
+        command: [DockerStubCommand.SUCCESS],
+      },
+    });
+
+    new AssetStaging(stack2, 'Asset', {
+      sourcePath: directory,
+      assetHashType: AssetHashType.OUTPUT,
+      bundling: {
+        image: DockerImage.fromRegistry('alpine'),
+        command: [DockerStubCommand.MULTIPLE_FILES],
+      },
+    });
+
+    // THEN
+    const dockerStubInput = readDockerStubInputConcat();
+    // Docker ran for the asset in Stack1
+    expect(dockerStubInput).toMatch(DockerStubCommand.SUCCESS);
+    // Docker ran for the asset in Stack2
+    expect(dockerStubInput).toMatch(DockerStubCommand.MULTIPLE_FILES);
+  });
+
+  test('correctly bundles with stack under stage and partial globstar wildcard', () => {
+    // GIVEN
+    const app = new App();
+
+    const stage = new Stage(app, 'Stage');
+    stage.node.setContext(cxapi.BUNDLING_STACKS, ['**/Stack1']); // a single wildcard prefix ('*Stack1') won't match
+
+    const stack1 = new Stack(stage, 'Stack1');
+    const stack2 = new Stack(stage, 'Stack2');
+    const directory = path.join(__dirname, 'fs', 'fixtures', 'test1');
+
+    // WHEN
+    new AssetStaging(stack1, 'Asset', {
+      sourcePath: directory,
+      assetHashType: AssetHashType.OUTPUT,
+      bundling: {
+        image: DockerImage.fromRegistry('alpine'),
+        command: [DockerStubCommand.SUCCESS],
+      },
+    });
+
+    new AssetStaging(stack2, 'Asset', {
+      sourcePath: directory,
+      assetHashType: AssetHashType.OUTPUT,
+      bundling: {
+        image: DockerImage.fromRegistry('alpine'),
+        command: [DockerStubCommand.MULTIPLE_FILES],
+      },
+    });
+
+    // THEN
+    const dockerStubInput = readDockerStubInputConcat();
+    // Docker ran for the asset in Stack1
+    expect(dockerStubInput).toMatch(DockerStubCommand.SUCCESS);
+    // Docker did not run for the asset in Stack2
+    expect(dockerStubInput).not.toMatch(DockerStubCommand.MULTIPLE_FILES);
+  });
+
+  test('correctly bundles selected stacks nested in Stack/Stage/Stack', () => {
+    // GIVEN
+    const app = new App();
+
+    const topStack = new Stack(app, 'TopStack');
+    topStack.node.setContext(cxapi.BUNDLING_STACKS, ['TopStack/MiddleStage/BottomStack']);
+
+    const middleStage = new Stage(topStack, 'MiddleStage');
+    const bottomStack = new Stack(middleStage, 'BottomStack');
+    const directory = path.join(__dirname, 'fs', 'fixtures', 'test1');
+
+    // WHEN
+    new AssetStaging(bottomStack, 'Asset', {
+      sourcePath: directory,
+      assetHashType: AssetHashType.OUTPUT,
+      bundling: {
+        image: DockerImage.fromRegistry('alpine'),
+        command: [DockerStubCommand.SUCCESS],
+      },
+    });
+    new AssetStaging(topStack, 'Asset', {
+      sourcePath: directory,
+      assetHashType: AssetHashType.OUTPUT,
+      bundling: {
+        image: DockerImage.fromRegistry('alpine'),
+        command: [DockerStubCommand.MULTIPLE_FILES],
+      },
+    });
+
+    const dockerStubInput = readDockerStubInputConcat();
+    // Docker ran for the asset in BottomStack
+    expect(dockerStubInput).toMatch(DockerStubCommand.SUCCESS);
+    // Docker did not run for the asset in TopStack
+    expect(dockerStubInput).not.toMatch(DockerStubCommand.MULTIPLE_FILES);
+  });
+
   test('bundling still occurs with partial wildcard', () => {
     // GIVEN
     const app = new App();
@@ -954,7 +1103,7 @@ describe('staging', () => {
     expect(asset.assetHash).toEqual('33cbf2cae5432438e0f046bc45ba8c3cef7b6afcf47b59d1c183775c1918fb1f'); // hash of MyStack/Asset
   });
 
-  test('bundling still occurs with full wildcard', () => {
+  test('bundling still occurs with a single wildcard', () => {
     // GIVEN
     const app = new App();
     const stack = new Stack(app, 'MyStack');
diff --git a/packages/aws-cdk/README.md b/packages/aws-cdk/README.md
index 57356153cf7b2..8ee36557dd51c 100644
--- a/packages/aws-cdk/README.md
+++ b/packages/aws-cdk/README.md
@@ -288,7 +288,7 @@ are written to the same output file where each stack artifact ID is a key in the
 
 
 ```console
-$ cdk deploy '*' --outputs-file "/Users/code/myproject/outputs.json"
+$ cdk deploy '**' --outputs-file "/Users/code/myproject/outputs.json"
 ```
 
 Example `outputs.json` after deployment of multiple stacks
diff --git a/packages/aws-cdk/lib/api/cxapp/exec.ts b/packages/aws-cdk/lib/api/cxapp/exec.ts
index 01259f7a11763..d4bb217135d59 100644
--- a/packages/aws-cdk/lib/api/cxapp/exec.ts
+++ b/packages/aws-cdk/lib/api/cxapp/exec.ts
@@ -44,7 +44,7 @@ export async function execProgram(aws: SdkProvider, config: Configuration): Prom
     context[cxapi.DISABLE_ASSET_STAGING_CONTEXT] = true;
   }
 
-  const bundlingStacks = config.settings.get(['bundlingStacks']) ?? ['*'];
+  const bundlingStacks = config.settings.get(['bundlingStacks']) ?? ['**'];
   context[cxapi.BUNDLING_STACKS] = bundlingStacks;
 
   debug('context:', context);
diff --git a/packages/aws-cdk/lib/settings.ts b/packages/aws-cdk/lib/settings.ts
index adb467e49b798..b94f563eb8365 100644
--- a/packages/aws-cdk/lib/settings.ts
+++ b/packages/aws-cdk/lib/settings.ts
@@ -256,8 +256,8 @@ export class Settings {
     // If we deploy, diff, synth or watch a list of stacks exclusively we skip
     // bundling for all other stacks.
       bundlingStacks = argv.exclusively
-        ? argv.STACKS ?? ['*']
-        : ['*'];
+        ? argv.STACKS ?? ['**']
+        : ['**'];
     } else { // Skip bundling for all stacks
       bundlingStacks = [];
     }
diff --git a/packages/aws-cdk/test/settings.test.ts b/packages/aws-cdk/test/settings.test.ts
index 8c2c894ae4634..3e0c6e49586ac 100644
--- a/packages/aws-cdk/test/settings.test.ts
+++ b/packages/aws-cdk/test/settings.test.ts
@@ -90,24 +90,24 @@ test('bundling stacks defaults to an empty list', () => {
   expect(settings.get(['bundlingStacks'])).toEqual([]);
 });
 
-test('bundling stacks defaults to * for deploy', () => {
+test('bundling stacks defaults to ** for deploy', () => {
   // GIVEN
   const settings = Settings.fromCommandLineArguments({
     _: [Command.DEPLOY],
   });
 
   // THEN
-  expect(settings.get(['bundlingStacks'])).toEqual(['*']);
+  expect(settings.get(['bundlingStacks'])).toEqual(['**']);
 });
 
-test('bundling stacks defaults to * for watch', () => {
+test('bundling stacks defaults to ** for watch', () => {
   // GIVEN
   const settings = Settings.fromCommandLineArguments({
     _: [Command.WATCH],
   });
 
   // THEN
-  expect(settings.get(['bundlingStacks'])).toEqual(['*']);
+  expect(settings.get(['bundlingStacks'])).toEqual(['**']);
 });
 
 test('bundling stacks with deploy exclusively', () => {
@@ -154,4 +154,4 @@ test('providing a build arg', () => {
 
   // THEN
   expect(settings.get(['build'])).toEqual('mvn package');
-});
\ No newline at end of file
+});