diff --git a/tests/test_cognitoidp/test_cognitoidp.py b/tests/test_cognitoidp/test_cognitoidp.py
index 5eb529e28..3b7037889 100644
--- a/tests/test_cognitoidp/test_cognitoidp.py
+++ b/tests/test_cognitoidp/test_cognitoidp.py
@@ -14,7 +14,7 @@ from botocore.exceptions import ClientError
 from jose import jws, jwk, jwt
 from nose.tools import assert_raises
 
-from moto import mock_cognitoidp
+from moto import mock_cognitoidp, settings
 from moto.core import ACCOUNT_ID
 
 
@@ -1312,52 +1312,58 @@ def test_admin_update_user_attributes():
             val.should.equal("Jane")
 
 
-@mock_cognitoidp
-def test_idtoken_contains_kid_header():
-    # https://github.com/spulec/moto/issues/3078
-    # Setup
-    cognito = boto3.client("cognito-idp", "us-west-2")
-    user_pool_id = cognito.create_user_pool(PoolName=str(uuid.uuid4()))["UserPool"][
-        "Id"
-    ]
-    client = cognito.create_user_pool_client(
-        UserPoolId=user_pool_id,
-        ExplicitAuthFlows=[
-            "ALLOW_ADMIN_USER_PASSWORD_AUTH",
-            "ALLOW_REFRESH_TOKEN_AUTH",
-            "ALLOW_ADMIN_NO_SRP_AUTH",
-        ],
-        AllowedOAuthFlows=["code", "implicit"],
-        ClientName=str(uuid.uuid4()),
-        CallbackURLs=["https://example.com"],
-    )
-    client_id = client["UserPoolClient"]["ClientId"]
-    username = str(uuid.uuid4())
-    temporary_password = "1TemporaryP@ssword"
-    cognito.admin_create_user(
-        UserPoolId=user_pool_id, Username=username, TemporaryPassword=temporary_password
-    )
-    result = cognito.admin_initiate_auth(
-        UserPoolId=user_pool_id,
-        ClientId=client_id,
-        AuthFlow="ADMIN_NO_SRP_AUTH",
-        AuthParameters={"USERNAME": username, "PASSWORD": temporary_password},
-    )
+# Test will retrieve public key from cognito.amazonaws.com/.well-known/jwks.json,
+# which isnt mocked in ServerMode
+if not settings.TEST_SERVER_MODE:
 
-    # A newly created user is forced to set a new password
-    # This sets a new password and logs the user in (creates tokens)
-    password = "1F@kePassword"
-    result = cognito.respond_to_auth_challenge(
-        Session=result["Session"],
-        ClientId=client_id,
-        ChallengeName="NEW_PASSWORD_REQUIRED",
-        ChallengeResponses={"USERNAME": username, "NEW_PASSWORD": password},
-    )
-    #
-    id_token = result["AuthenticationResult"]["IdToken"]
+    @mock_cognitoidp
+    def test_idtoken_contains_kid_header():
+        # https://github.com/spulec/moto/issues/3078
+        # Setup
+        cognito = boto3.client("cognito-idp", "us-west-2")
+        user_pool_id = cognito.create_user_pool(PoolName=str(uuid.uuid4()))["UserPool"][
+            "Id"
+        ]
+        client = cognito.create_user_pool_client(
+            UserPoolId=user_pool_id,
+            ExplicitAuthFlows=[
+                "ALLOW_ADMIN_USER_PASSWORD_AUTH",
+                "ALLOW_REFRESH_TOKEN_AUTH",
+                "ALLOW_ADMIN_NO_SRP_AUTH",
+            ],
+            AllowedOAuthFlows=["code", "implicit"],
+            ClientName=str(uuid.uuid4()),
+            CallbackURLs=["https://example.com"],
+        )
+        client_id = client["UserPoolClient"]["ClientId"]
+        username = str(uuid.uuid4())
+        temporary_password = "1TemporaryP@ssword"
+        cognito.admin_create_user(
+            UserPoolId=user_pool_id,
+            Username=username,
+            TemporaryPassword=temporary_password,
+        )
+        result = cognito.admin_initiate_auth(
+            UserPoolId=user_pool_id,
+            ClientId=client_id,
+            AuthFlow="ADMIN_NO_SRP_AUTH",
+            AuthParameters={"USERNAME": username, "PASSWORD": temporary_password},
+        )
 
-    # Verify the KID header is present in the token, and corresponds to the KID supplied by the public JWT
-    verify_kid_header(id_token)
+        # A newly created user is forced to set a new password
+        # This sets a new password and logs the user in (creates tokens)
+        password = "1F@kePassword"
+        result = cognito.respond_to_auth_challenge(
+            Session=result["Session"],
+            ClientId=client_id,
+            ChallengeName="NEW_PASSWORD_REQUIRED",
+            ChallengeResponses={"USERNAME": username, "NEW_PASSWORD": password},
+        )
+        #
+        id_token = result["AuthenticationResult"]["IdToken"]
+
+        # Verify the KID header is present in the token, and corresponds to the KID supplied by the public JWT
+        verify_kid_header(id_token)
 
 
 def verify_kid_header(token):