diff --git a/packages/@aws-cdk/cloudformation-include/test/test-templates/fn-select-with-novalue.json b/packages/@aws-cdk/cloudformation-include/test/test-templates/fn-select-with-novalue.json
new file mode 100644
index 0000000000000..861387e330ee7
--- /dev/null
+++ b/packages/@aws-cdk/cloudformation-include/test/test-templates/fn-select-with-novalue.json
@@ -0,0 +1,23 @@
+{
+  "Parameters": {
+    "DoIt": {
+      "Type": "String"
+    }
+  },
+  "Conditions": {
+    "MyCondition": {
+      "Fn::Equals": [{ "Ref": "DoIt" }, "Yes"]
+    }
+  },
+  "Resources": {
+    "Bucket": {
+      "Type": "AWS::S3::Bucket",
+      "Properties": {
+        "BucketName": { "Fn::Select": [0, [
+          { "Fn::If": ["MyCondition", "doing-it", { "Ref": "AWS::NoValue" }] },
+          "not-doingit"
+        ]]}
+      }
+    }
+  }
+}
diff --git a/packages/@aws-cdk/cloudformation-include/test/valid-templates.test.ts b/packages/@aws-cdk/cloudformation-include/test/valid-templates.test.ts
index 65cd7e981cc81..eec714ac5d7d6 100644
--- a/packages/@aws-cdk/cloudformation-include/test/valid-templates.test.ts
+++ b/packages/@aws-cdk/cloudformation-include/test/valid-templates.test.ts
@@ -1081,6 +1081,14 @@ describe('CDK Include', () => {
       loadTestFileToJsObject('properties-not-in-cfn-spec.json'),
     );
   });
+
+  test('roundtrip a fn-select with a fn-if/ref-novalue in it', () => {
+    includeTestTemplate(stack, 'fn-select-with-novalue.json');
+
+    Template.fromStack(stack).templateMatches(
+      loadTestFileToJsObject('fn-select-with-novalue.json'),
+    );
+  });
 });
 
 interface IncludeTestTemplateProps {
diff --git a/packages/@aws-cdk/core/lib/cfn-fn.ts b/packages/@aws-cdk/core/lib/cfn-fn.ts
index 3ef1c265654bd..673784e0e2a5b 100644
--- a/packages/@aws-cdk/core/lib/cfn-fn.ts
+++ b/packages/@aws-cdk/core/lib/cfn-fn.ts
@@ -127,7 +127,7 @@ export class Fn {
    * @returns a token represented as a string
    */
   public static select(index: number, array: string[]): string {
-    if (!Token.isUnresolved(array)) {
+    if (!Token.isUnresolved(index) && !Token.isUnresolved(array) && !array.some(Token.isUnresolved)) {
       return array[index];
     }
 
diff --git a/packages/@aws-cdk/core/test/fn.test.ts b/packages/@aws-cdk/core/test/fn.test.ts
index 221a7b6e811a1..343c3e0ea0422 100644
--- a/packages/@aws-cdk/core/test/fn.test.ts
+++ b/packages/@aws-cdk/core/test/fn.test.ts
@@ -1,6 +1,6 @@
 import * as fc from 'fast-check';
 import * as _ from 'lodash';
-import { App, CfnOutput, Fn, Stack, Token } from '../lib';
+import { App, Aws, CfnOutput, Fn, Stack, Token } from '../lib';
 import { Intrinsic } from '../lib/private/intrinsic';
 
 function asyncTest(cb: () => Promise<void>): () => void {
@@ -27,8 +27,24 @@ describe('fn', () => {
   describe('eager resolution for non-tokens', () => {
     test('Fn.select', () => {
       expect(Fn.select(2, ['hello', 'you', 'dude'])).toEqual('dude');
+    });
+
+    test('Fn.select does not short-circuit if there are tokens in the array', () => {
+      const stack = new Stack();
 
+      expect(stack.resolve(Fn.select(2, [
+        Fn.conditionIf('xyz', 'yep', Aws.NO_VALUE).toString(),
+        'you',
+        'dude',
+      ]))).toEqual({
+        'Fn::Select': [2, [
+          { 'Fn::If': ['xyz', 'yep', { Ref: 'AWS::NoValue' }] },
+          'you',
+          'dude',
+        ]],
+      });
     });
+
     test('Fn.split', () => {
       expect(Fn.split(':', 'hello:world:yeah')).toEqual(['hello', 'world', 'yeah']);