diff --git a/packages/aws-cdk/test/integ/cli.exclusions.js b/packages/aws-cdk/test/integ/cli.exclusions.js
index 6c9d25a778e4c..b4255505e2bcf 100644
--- a/packages/aws-cdk/test/integ/cli.exclusions.js
+++ b/packages/aws-cdk/test/integ/cli.exclusions.js
@@ -15,20 +15,10 @@ For example:
 
 */
 const exclusions = [
-  {
-    "test": "test-cdk-deploy-with-parameters.sh",
-    "version": "v1.31.0",
-    "justification": "This test doesn't use a unique sns topic name and it collides with our regular integ suite"
-  },
-  {
-    "test": "test-cdk-deploy-wildcard-with-parameters.sh",
-    "version": "v1.31.0",
-    "justification": "This test doesn't use a unique sns topic name and it collides with our regular integ suite"
-  },
   {
     "test": "test-cdk-deploy-nested-stack-with-parameters.sh",
-    "version": "v1.31.0",
-    "justification": "This test doesn't use a unique sns topic name and it collides with our regular integ suite"
+    "version": "v1.37.0",
+    "justification": "This test doesn't use a unique sns topic name for the topic in the nested stack and it collides with our regular integ suite"
   }
 ]
 
diff --git a/packages/aws-cdk/test/integ/cli/app/app.js b/packages/aws-cdk/test/integ/cli/app/app.js
index 0344c834d0a1c..5fdfcbfd0c10c 100644
--- a/packages/aws-cdk/test/integ/cli/app/app.js
+++ b/packages/aws-cdk/test/integ/cli/app/app.js
@@ -46,7 +46,7 @@ class ParameterStack extends cdk.Stack {
     super(parent, id, props);
 
     new sns.Topic(this, 'TopicParameter', {
-      topicName: new cdk.CfnParameter(this, 'TopicNameParam')
+      topicName: new cdk.CfnParameter(this, 'TopicNameParam').valueAsString
     });
   }
 }
@@ -56,7 +56,7 @@ class OtherParameterStack extends cdk.Stack {
     super(parent, id, props);
 
     new sns.Topic(this, 'TopicParameter', {
-      topicName: new cdk.CfnParameter(this, 'OtherTopicNameParam')
+      topicName: new cdk.CfnParameter(this, 'OtherTopicNameParam').valueAsString
     });
   }
 }
@@ -66,10 +66,10 @@ class MultiParameterStack extends cdk.Stack {
     super(parent, id, props);
 
     new sns.Topic(this, 'TopicParameter', {
-      displayName: new cdk.CfnParameter(this, 'DisplayNameParam')
+      displayName: new cdk.CfnParameter(this, 'DisplayNameParam').valueAsString
     });
     new sns.Topic(this, 'OtherTopicParameter', {
-      displayName: new cdk.CfnParameter(this, 'OtherDisplayNameParam')
+      displayName: new cdk.CfnParameter(this, 'OtherDisplayNameParam').valueAsString
     });
   }
 }
diff --git a/packages/aws-cdk/test/integ/cli/app/nested-stack.js b/packages/aws-cdk/test/integ/cli/app/nested-stack.js
index 98202ee4520e5..3b3125963679b 100644
--- a/packages/aws-cdk/test/integ/cli/app/nested-stack.js
+++ b/packages/aws-cdk/test/integ/cli/app/nested-stack.js
@@ -20,9 +20,9 @@ class MyNestedStack extends cfn.NestedStack {
 class StackWithNestedStackUsingParameters extends Stack {
   constructor(scope, id) {
     super(scope, id);
-    new CfnParameter(this, 'MyTopicParam');
+    const topicNameParam = new CfnParameter(this, 'MyTopicParam');
     new MyNestedStackUsingParameters(this, 'MyNested', {
-      parameters: {'MyTopicParam': 'ThereIsASpoon'}
+      parameters: {'MyTopicParam': topicNameParam.valueAsString}
     });
   }
 }