diff --git a/packages/@aws-cdk/aws-cloudformation/test/integ.nested-stacks-multi-refs.ts b/packages/@aws-cdk/aws-cloudformation/test/integ.nested-stacks-multi-refs.ts
index f133d07bea8c9..b64a4d488e956 100644
--- a/packages/@aws-cdk/aws-cloudformation/test/integ.nested-stacks-multi-refs.ts
+++ b/packages/@aws-cdk/aws-cloudformation/test/integ.nested-stacks-multi-refs.ts
@@ -1,3 +1,4 @@
+/// !cdk-integ pragma:ignore-assets
 import * as sns from '@aws-cdk/aws-sns';
 import { App, Fn, Stack } from '@aws-cdk/core';
 import { NestedStack } from '../lib';
@@ -28,4 +29,4 @@ app.synth();
 // Stack1-NestedUnderStack1NestedStackNestedUnderStack1NestedStackResourceF616305B-EM64TEGA04J9-TopicInNestedUnderStack115E329C4-HEO7NLYC1AFL
 function shortName(topicName: string) {
   return Fn.select(1, Fn.split('-', topicName));
-}
\ No newline at end of file
+}
diff --git a/packages/@aws-cdk/aws-cloudformation/test/integ.nested-stacks-multi.ts b/packages/@aws-cdk/aws-cloudformation/test/integ.nested-stacks-multi.ts
index b3e51a8c049f1..109b151138b19 100644
--- a/packages/@aws-cdk/aws-cloudformation/test/integ.nested-stacks-multi.ts
+++ b/packages/@aws-cdk/aws-cloudformation/test/integ.nested-stacks-multi.ts
@@ -1,3 +1,4 @@
+/// !cdk-integ pragma:ignore-assets
 import * as sns from '@aws-cdk/aws-sns';
 import { App, Construct, Stack } from '@aws-cdk/core';
 import * as cfn from '../lib';
diff --git a/packages/@aws-cdk/aws-cloudformation/test/test.nested-stack.ts b/packages/@aws-cdk/aws-cloudformation/test/test.nested-stack.ts
index de102b4b1cf51..5f809e7e544bf 100644
--- a/packages/@aws-cdk/aws-cloudformation/test/test.nested-stack.ts
+++ b/packages/@aws-cdk/aws-cloudformation/test/test.nested-stack.ts
@@ -3,7 +3,7 @@ import * as path from 'path';
 import { expect, haveResource, matchTemplate, SynthUtils } from '@aws-cdk/assert';
 import * as s3_assets from '@aws-cdk/aws-s3-assets';
 import * as sns from '@aws-cdk/aws-sns';
-import { App, CfnParameter, CfnResource, Construct, ContextProvider, Stack } from '@aws-cdk/core';
+import { App, CfnParameter, CfnResource, Construct, ContextProvider, LegacyStackSynthesizer, Stack } from '@aws-cdk/core';
 import { Test } from 'nodeunit';
 import { NestedStack } from '../lib/nested-stack';
 
@@ -714,6 +714,8 @@ export = {
       },
     });
 
+    const middleStackHash = 'b2670b4c0c3fdf1d8fd9b9272bb8bf8173d18c0f67a888ba165cc569a248a84f';
+
     // nested1 wires the nested2 template through parameters, so we expect those
     expect(nested1).to(haveResource('Resource::1'));
     const nested2Template = SynthUtils.toCloudFormation(nested1);
@@ -729,9 +731,9 @@ export = {
       AssetParameters8169c6f8aaeaf5e2e8620f5f895ffe2099202ccb4b6889df48fe0967a894235cS3BucketDE3B88D6: { Type: 'String', Description: 'S3 bucket for asset "8169c6f8aaeaf5e2e8620f5f895ffe2099202ccb4b6889df48fe0967a894235c"' },
       AssetParameters8169c6f8aaeaf5e2e8620f5f895ffe2099202ccb4b6889df48fe0967a894235cS3VersionKey3A62EFEA: { Type: 'String', Description: 'S3 key for asset version "8169c6f8aaeaf5e2e8620f5f895ffe2099202ccb4b6889df48fe0967a894235c"' },
       AssetParameters8169c6f8aaeaf5e2e8620f5f895ffe2099202ccb4b6889df48fe0967a894235cArtifactHash7DC546E0: { Type: 'String', Description: 'Artifact hash for asset "8169c6f8aaeaf5e2e8620f5f895ffe2099202ccb4b6889df48fe0967a894235c"' },
-      AssetParameters8b50795a950cca6b01352f162c45d9d274dee6bc409f2f2b2ed029ad6828b3bfS3Bucket76ACFB38: { Type: 'String', Description: 'S3 bucket for asset "8b50795a950cca6b01352f162c45d9d274dee6bc409f2f2b2ed029ad6828b3bf"' },
-      AssetParameters8b50795a950cca6b01352f162c45d9d274dee6bc409f2f2b2ed029ad6828b3bfS3VersionKey04162EF1: { Type: 'String', Description: 'S3 key for asset version "8b50795a950cca6b01352f162c45d9d274dee6bc409f2f2b2ed029ad6828b3bf"' },
-      AssetParameters8b50795a950cca6b01352f162c45d9d274dee6bc409f2f2b2ed029ad6828b3bfArtifactHashF227ADD3: { Type: 'String', Description: 'Artifact hash for asset "8b50795a950cca6b01352f162c45d9d274dee6bc409f2f2b2ed029ad6828b3bf"' },
+      [`AssetParameters${middleStackHash}S3Bucket3DB431CB`]: { Type: 'String', Description: `S3 bucket for asset "${middleStackHash}"` },
+      [`AssetParameters${middleStackHash}S3VersionKeyBFFDABE9`]: { Type: 'String', Description: `S3 key for asset version "${middleStackHash}"` },
+      [`AssetParameters${middleStackHash}ArtifactHash8EA52875`]: { Type: 'String', Description: `Artifact hash for asset "${middleStackHash}"` },
     });
 
     // proxy asset params to nested stack
@@ -935,6 +937,37 @@ export = {
     test.done();
   },
 
+  '3-level stacks: legacy synthesizer parameters are added to the middle-level stack'(test: Test) {
+    // GIVEN
+    const app = new App();
+    const top = new Stack(app, 'stack', {
+      synthesizer: new LegacyStackSynthesizer(),
+    });
+    const middle = new NestedStack(top, 'nested1');
+    const bottom = new NestedStack(middle, 'nested2');
+
+    // WHEN
+    new CfnResource(bottom, 'Something', {
+      type: 'BottomLevel',
+    });
+
+    // THEN
+    const asm = app.synth();
+    const middleTemplate = JSON.parse(fs.readFileSync(path.join(asm.directory, middle.templateFile), { encoding: 'utf-8' }));
+
+    const hash = 'bc3c51e4d3545ee0a0069401e5a32c37b66d044b983f12de416ba1576ecaf0a4';
+    test.deepEqual(middleTemplate.Parameters ?? {}, {
+      [`referencetostackAssetParameters${hash}S3BucketD7C30435Ref`]: {
+        Type: 'String',
+      },
+      [`referencetostackAssetParameters${hash}S3VersionKeyB667DBE1Ref`]: {
+        Type: 'String',
+      },
+    });
+
+    test.done();
+  },
+
   'references to a resource from a deeply nested stack'(test: Test) {
     // GIVEN
     const app = new App();
diff --git a/packages/@aws-cdk/cloudformation-include/test/nested-stacks.test.ts b/packages/@aws-cdk/cloudformation-include/test/nested-stacks.test.ts
index bf729dcedd38b..0e9dcadc5ce60 100644
--- a/packages/@aws-cdk/cloudformation-include/test/nested-stacks.test.ts
+++ b/packages/@aws-cdk/cloudformation-include/test/nested-stacks.test.ts
@@ -444,6 +444,9 @@ describe('CDK Include for nested stacks', () => {
     let child: inc.IncludedNestedStack;
     let grandChild: inc.IncludedNestedStack;
 
+    let hash1: string;
+    let hash2: string;
+
     let parentBucketParam: string;
     let parentKeyParam: string;
     let grandChildBucketParam: string;
@@ -471,13 +474,16 @@ describe('CDK Include for nested stacks', () => {
       child = parentTemplate.getNestedStack('ChildStack');
       grandChild = child.includedTemplate.getNestedStack('GrandChildStack');
 
-      parentBucketParam = 'AssetParameters5dc7d4a99cfe2979687dc74f2db9fd75f253b5505a1912b5ceecf70c9aefba50S3BucketEAA24F0C';
-      parentKeyParam = 'AssetParameters5dc7d4a99cfe2979687dc74f2db9fd75f253b5505a1912b5ceecf70c9aefba50S3VersionKey1194CAB2';
-      grandChildBucketParam = 'referencetoAssetParameters5dc7d4a99cfe2979687dc74f2db9fd75f253b5505a1912b5ceecf70c9aefba50S3BucketEAA24F0CRef';
-      grandChildKeyParam = 'referencetoAssetParameters5dc7d4a99cfe2979687dc74f2db9fd75f253b5505a1912b5ceecf70c9aefba50S3VersionKey1194CAB2Ref';
+      hash1 = '5dc7d4a99cfe2979687dc74f2db9fd75f253b5505a1912b5ceecf70c9aefba50';
+      hash2 = '7775730164edb5faae717ac1d2e90d9c0d0fdbeafe48763e5c1b7fb5e39e00a5';
+
+      parentBucketParam = `AssetParameters${hash1}S3BucketEAA24F0C`;
+      parentKeyParam = `AssetParameters${hash1}S3VersionKey1194CAB2`;
+      grandChildBucketParam = `referencetoAssetParameters${hash1}S3BucketEAA24F0CRef`;
+      grandChildKeyParam = `referencetoAssetParameters${hash1}S3VersionKey1194CAB2Ref`;
 
-      childBucketParam = 'AssetParameters891fd3ec75dc881b0fe40dc9fd1b433672637585c015265a5f0dab6bf79818d5S3Bucket23278F13';
-      childKeyParam = 'AssetParameters891fd3ec75dc881b0fe40dc9fd1b433672637585c015265a5f0dab6bf79818d5S3VersionKey7316205A';
+      childBucketParam = `AssetParameters${hash2}S3BucketDEB194C6`;
+      childKeyParam = `AssetParameters${hash2}S3VersionKey8B342ED1`;
     });
 
     test('correctly creates parameters in the parent stack, and passes them to the child stack', () => {
@@ -485,27 +491,27 @@ describe('CDK Include for nested stacks', () => {
         "Parameters": {
           [parentBucketParam]: {
             "Type": "String",
-            "Description": "S3 bucket for asset \"5dc7d4a99cfe2979687dc74f2db9fd75f253b5505a1912b5ceecf70c9aefba50\"",
+            "Description": `S3 bucket for asset \"${hash1}\"`,
           },
           [parentKeyParam]: {
             "Type": "String",
-            "Description": "S3 key for asset version \"5dc7d4a99cfe2979687dc74f2db9fd75f253b5505a1912b5ceecf70c9aefba50\"",
+            "Description": `S3 key for asset version \"${hash1}\"`,
           },
-          "AssetParameters5dc7d4a99cfe2979687dc74f2db9fd75f253b5505a1912b5ceecf70c9aefba50ArtifactHash9C417847": {
+          [`AssetParameters${hash1}ArtifactHash9C417847`]: {
             "Type": "String",
-            "Description": "Artifact hash for asset \"5dc7d4a99cfe2979687dc74f2db9fd75f253b5505a1912b5ceecf70c9aefba50\"",
+            "Description": `Artifact hash for asset \"${hash1}\"`,
           },
           [childBucketParam]: {
             "Type": "String",
-            "Description": "S3 bucket for asset \"891fd3ec75dc881b0fe40dc9fd1b433672637585c015265a5f0dab6bf79818d5\"",
+            "Description": `S3 bucket for asset \"${hash2}\"`,
           },
           [childKeyParam]: {
             "Type": "String",
-            "Description": "S3 key for asset version \"891fd3ec75dc881b0fe40dc9fd1b433672637585c015265a5f0dab6bf79818d5\"",
+            "Description": `S3 key for asset version \"${hash2}\"`,
           },
-          "AssetParameters891fd3ec75dc881b0fe40dc9fd1b433672637585c015265a5f0dab6bf79818d5ArtifactHashA1DE5198": {
+          [`AssetParameters${hash2}ArtifactHashAA82D4CC`]: {
             "Type": "String",
-            "Description": "Artifact hash for asset \"891fd3ec75dc881b0fe40dc9fd1b433672637585c015265a5f0dab6bf79818d5\"",
+            "Description": `Artifact hash for asset \"${hash2}\"`,
           },
         },
         "Resources": {
diff --git a/packages/@aws-cdk/core/lib/private/prepare-app.ts b/packages/@aws-cdk/core/lib/private/prepare-app.ts
index ad900acf803c0..e90a40ff211f8 100644
--- a/packages/@aws-cdk/core/lib/private/prepare-app.ts
+++ b/packages/@aws-cdk/core/lib/private/prepare-app.ts
@@ -28,19 +28,32 @@ export function prepareApp(root: IConstruct) {
     }
   }
 
+  resolveReferences(root);
+
   // depth-first (children first) queue of nested stacks. We will pop a stack
   // from the head of this queue to prepare its template asset.
+  //
+  // Depth-first since the a nested stack's template hash will be reflected in
+  // its parent's template, which then changes the parent's hash, etc.
   const queue = findAllNestedStacks(root);
 
-  while (true) {
-    resolveReferences(root);
-
-    const nested = queue.shift();
-    if (!nested) {
-      break;
+  if (queue.length > 0) {
+    while (queue.length > 0) {
+      const nested = queue.shift()!;
+      defineNestedStackAsset(nested);
     }
 
-    defineNestedStackAsset(nested);
+    // ▷[ Given the legacy synthesizer and a 3-or-deeper nesting of nested stacks ]
+    //
+    // Adding nested stack assets may haved added CfnParameters to the top-level
+    // stack which are referenced in a deeper-level stack. The values of these
+    // parameters need to be carried through to the right location via Nested
+    // Stack parameters, which `resolveReferences()` will do.
+    //
+    // Yes, this may add `Parameter` elements to a template whose hash has
+    // already been calculated, but the invariant that if the functional part
+    // of the template changes its hash will change is still upheld.
+    resolveReferences(root);
   }
 }