diff --git a/x-pack/plugin/core/src/main/java/org/elasticsearch/xpack/core/ml/utils/MlIndexAndAlias.java b/x-pack/plugin/core/src/main/java/org/elasticsearch/xpack/core/ml/utils/MlIndexAndAlias.java
index 5c98904095740..82d5780ae9066 100644
--- a/x-pack/plugin/core/src/main/java/org/elasticsearch/xpack/core/ml/utils/MlIndexAndAlias.java
+++ b/x-pack/plugin/core/src/main/java/org/elasticsearch/xpack/core/ml/utils/MlIndexAndAlias.java
@@ -118,7 +118,7 @@ public static void createIndexAndAliasIfNecessary(Client client,
         // The initial index name must be suitable for rollover functionality.
         String firstConcreteIndex = indexPatternPrefix + "-000001";
         String[] concreteIndexNames =
-            resolver.concreteIndexNames(clusterState, IndicesOptions.lenientExpandOpen(), indexPattern);
+            resolver.concreteIndexNames(clusterState, IndicesOptions.lenientExpandHidden(), indexPattern);
         Optional<IndexMetadata> indexPointedByCurrentWriteAlias = clusterState.getMetadata().hasAlias(alias)
             ? clusterState.getMetadata().getIndicesLookup().get(alias).getIndices().stream().findFirst()
             : Optional.empty();
@@ -241,11 +241,17 @@ private static void createFirstConcreteIndex(Client client,
             ActionListener.<CreateIndexResponse>wrap(
                 createIndexResponse -> listener.onResponse(true),
                 createIndexFailure -> {
-                    // If it was created between our last check, and this request being handled, we should add the alias
-                    // Adding an alias that already exists is idempotent. So, no need to double check if the alias exists
-                    // as well.
                     if (ExceptionsHelper.unwrapCause(createIndexFailure) instanceof ResourceAlreadyExistsException) {
-                        updateWriteAlias(client, alias, null, index, listener);
+                        // If it was created between our last check and this request being handled, we should add the alias
+                        // if we were asked to add it on creation.  Adding an alias that already exists is idempotent. So
+                        // no need to double check if the alias exists as well.  But if we weren't asked to add the alias
+                        // on creation then we should leave it up to the caller to decide what to do next (some call sites
+                        // already have more advanced alias update logic in their success handlers).
+                        if (addAlias) {
+                            updateWriteAlias(client, alias, null, index, listener);
+                        } else {
+                            listener.onResponse(true);
+                        }
                     } else {
                         listener.onFailure(createIndexFailure);
                     }
diff --git a/x-pack/plugin/ml/src/internalClusterTest/java/org/elasticsearch/xpack/ml/integration/JobStorageDeletionTaskIT.java b/x-pack/plugin/ml/src/internalClusterTest/java/org/elasticsearch/xpack/ml/integration/JobStorageDeletionTaskIT.java
index 061023f04e457..3b3ea7696b9a7 100644
--- a/x-pack/plugin/ml/src/internalClusterTest/java/org/elasticsearch/xpack/ml/integration/JobStorageDeletionTaskIT.java
+++ b/x-pack/plugin/ml/src/internalClusterTest/java/org/elasticsearch/xpack/ml/integration/JobStorageDeletionTaskIT.java
@@ -54,7 +54,7 @@
  */
 public class JobStorageDeletionTaskIT extends BaseMlIntegTestCase {
 
-    private static long bucketSpan = AnalysisConfig.Builder.DEFAULT_BUCKET_SPAN.getMillis();
+    private static final long bucketSpan = AnalysisConfig.Builder.DEFAULT_BUCKET_SPAN.getMillis();
     private static final String UNRELATED_INDEX = "unrelated-data";
 
     private JobResultsProvider jobResultsProvider;
@@ -179,7 +179,7 @@ public void testDeleteDedicatedJobWithDataInShared() throws Exception {
             .indices()
             .prepareGetIndex()
             .setIndices(dedicatedIndex)
-            .setIndicesOptions(IndicesOptions.LENIENT_EXPAND_OPEN)
+            .setIndicesOptions(IndicesOptions.LENIENT_EXPAND_OPEN_CLOSED_HIDDEN)
             .get()
             .indices().length, equalTo(0));