diff --git a/packages/@aws-cdk/aws-msk-alpha/README.md b/packages/@aws-cdk/aws-msk-alpha/README.md
index 81b74be3aa279..8155f8829a756 100644
--- a/packages/@aws-cdk/aws-msk-alpha/README.md
+++ b/packages/@aws-cdk/aws-msk-alpha/README.md
@@ -217,7 +217,8 @@ You can configure an MSK cluster storage mode using the `storageMode` property.
 Tiered storage is a low-cost storage tier for Amazon MSK that scales to virtually unlimited storage,
 making it cost-effective to build streaming data applications.
 
-> Visit [Tiered storage](https://docs.aws.amazon.com/msk/latest/developerguide/msk-tiered-storage.html) for more details.
+> Visit [Tiered storage](https://docs.aws.amazon.com/msk/latest/developerguide/msk-tiered-storage.html)
+to see the list of compatible Kafka versions and for more details.
 
 ```ts
 declare const vpc: ec2.Vpc;
@@ -225,7 +226,7 @@ declare const bucket: s3.IBucket;
 
 const cluster = new msk.Cluster(this, 'cluster', {
   clusterName: 'myCluster',
-  kafkaVersion: msk.KafkaVersion.V2_8_2_TIERED,
+  kafkaVersion: msk.KafkaVersion.V3_6_0,
   vpc,
   storageMode: msk.StorageMode.TIERED,
 });
diff --git a/packages/@aws-cdk/aws-msk-alpha/lib/cluster-version.ts b/packages/@aws-cdk/aws-msk-alpha/lib/cluster-version.ts
index 405c0c6ee0ecc..b3c5277018b1c 100644
--- a/packages/@aws-cdk/aws-msk-alpha/lib/cluster-version.ts
+++ b/packages/@aws-cdk/aws-msk-alpha/lib/cluster-version.ts
@@ -11,6 +11,15 @@ export class KafkaVersion {
    */
   public static readonly V1_1_1 = KafkaVersion.of('1.1.1');
 
+  /**
+   * **Deprecated by Amazon MSK. You can't create a Kafka cluster with a deprecated version.**
+   *
+   * Kafka version 2.1.0
+   *
+   * @deprecated use the latest runtime instead
+   */
+  public static readonly V2_1_0 = KafkaVersion.of('2.1.0');
+
   /**
    * Kafka version 2.2.1
    */
@@ -21,6 +30,15 @@ export class KafkaVersion {
    */
   public static readonly V2_3_1 = KafkaVersion.of('2.3.1');
 
+  /**
+   * **Deprecated by Amazon MSK. You can't create a Kafka cluster with a deprecated version.**
+   *
+   * Kafka version 2.4.1
+   *
+   * @deprecated use the latest runtime instead
+   */
+  public static readonly V2_4_1 = KafkaVersion.of('2.4.1');
+
   /**
    * Kafka version 2.4.1
    */
@@ -111,6 +129,11 @@ export class KafkaVersion {
    */
   public static readonly V3_5_1 = KafkaVersion.of('3.5.1');
 
+  /**
+   * Kafka version 3.6.0
+   */
+  public static readonly V3_6_0 = KafkaVersion.of('3.6.0');
+
   /**
    * Custom cluster version
    * @param version custom version number
@@ -119,6 +142,16 @@ export class KafkaVersion {
     return new KafkaVersion(version);
   }
 
+  /**
+   * List of Kafka versions that support tiered storage
+   *
+   * @see https://docs.aws.amazon.com/msk/latest/developerguide/msk-tiered-storage.html#msk-tiered-storage-requirements
+   */
+  private static readonly TIERED_STORAGE_COMPATIBLE_VERSIONS = [
+    KafkaVersion.V2_8_2_TIERED,
+    KafkaVersion.V3_6_0,
+  ].map(({ version }) => version);
+
   /**
    *
    * @param version cluster version number
@@ -129,6 +162,6 @@ export class KafkaVersion {
    * Checks if the cluster version supports tiered storage mode.
    */
   public isTieredStorageCompatible() {
-    return this.version.endsWith('.tiered');
+    return KafkaVersion.TIERED_STORAGE_COMPATIBLE_VERSIONS.includes(this.version);
   };
 }
diff --git a/packages/@aws-cdk/aws-msk-alpha/test/cluster.test.ts b/packages/@aws-cdk/aws-msk-alpha/test/cluster.test.ts
index babbb235b40a3..7c4bd6a10f4ec 100644
--- a/packages/@aws-cdk/aws-msk-alpha/test/cluster.test.ts
+++ b/packages/@aws-cdk/aws-msk-alpha/test/cluster.test.ts
@@ -790,6 +790,12 @@ describe('MSK Cluster', () => {
 
   describe('created with storage mode', () => {
     describe('with tiered storage mode', () => {
+      test('version.isTieredStorageCompatible', () => {
+        expect(msk.KafkaVersion.V2_8_2_TIERED.isTieredStorageCompatible()).toBeTruthy();
+        expect(msk.KafkaVersion.V3_5_1.isTieredStorageCompatible()).toBeFalsy();
+        expect(msk.KafkaVersion.V3_6_0.isTieredStorageCompatible()).toBeTruthy();
+      });
+
       test('create a cluster with tiered storage mode', () => {
         new msk.Cluster(stack, 'Cluster', {
           clusterName: 'cluster',
@@ -797,7 +803,7 @@ describe('MSK Cluster', () => {
           kafkaVersion: msk.KafkaVersion.V2_8_2_TIERED,
           vpc,
           storageMode: msk.StorageMode.TIERED,
-        }),
+        });
         Template.fromStack(stack).hasResourceProperties('AWS::MSK::Cluster', {
           StorageMode: 'TIERED',
         });