diff --git a/qa/ml-native-tests/src/test/java/org/elasticsearch/xpack/ml/integration/AutodetectMemoryLimitIT.java b/qa/ml-native-tests/src/test/java/org/elasticsearch/xpack/ml/integration/AutodetectMemoryLimitIT.java
index d2abcfe98b6..cfb1fe56e43 100644
--- a/qa/ml-native-tests/src/test/java/org/elasticsearch/xpack/ml/integration/AutodetectMemoryLimitIT.java
+++ b/qa/ml-native-tests/src/test/java/org/elasticsearch/xpack/ml/integration/AutodetectMemoryLimitIT.java
@@ -37,6 +37,7 @@ public class AutodetectMemoryLimitIT extends MlNativeAutodetectIntegTestCase {
         cleanUp();
     }
 
+    @AwaitsFix(bugUrl = "https://github.com/elastic/x-pack-elasticsearch/pull/4033")
     public void testTooManyPartitions() throws Exception {
         Detector.Builder detector = new Detector.Builder("count", null);
         detector.setPartitionFieldName("user");
@@ -91,6 +92,7 @@ public class AutodetectMemoryLimitIT extends MlNativeAutodetectIntegTestCase {
         assertThat(modelSizeStats.getMemoryStatus(), equalTo(ModelSizeStats.MemoryStatus.HARD_LIMIT));
     }
 
+    @AwaitsFix(bugUrl = "https://github.com/elastic/x-pack-elasticsearch/pull/4033")
     public void testTooManyByFields() throws Exception {
         Detector.Builder detector = new Detector.Builder("count", null);
         detector.setByFieldName("user");