diff --git a/stacksets/datadog-shipping/logs-template.yaml b/stacksets/datadog-shipping/logs-template.yaml
index 342b84d..17eaaaa 100644
--- a/stacksets/datadog-shipping/logs-template.yaml
+++ b/stacksets/datadog-shipping/logs-template.yaml
@@ -98,7 +98,7 @@ Resources:
           - Effect: Allow
             Action:
               - logs:PutLogEvents
-            Resource: !Sub "arn:aws:logs:${AWS::Region}:${AWS::AccountId}:log-group:/aws/kinesisfirehose/${AWS::StackName}:log-stream:*"
+            Resource: !GetAtt DeliveryStreamLogGroup.Arn
           - Effect: Allow
             Action:
               - kinesis:DescribeStream