diff --git a/x-pack/plugin/ilm/qa/multi-node/src/javaRestTest/java/org/elasticsearch/xpack/TimeSeriesRestDriver.java b/x-pack/plugin/ilm/qa/multi-node/src/javaRestTest/java/org/elasticsearch/xpack/TimeSeriesRestDriver.java
index a1c7ebc2d8b2c..11edfff9ee108 100644
--- a/x-pack/plugin/ilm/qa/multi-node/src/javaRestTest/java/org/elasticsearch/xpack/TimeSeriesRestDriver.java
+++ b/x-pack/plugin/ilm/qa/multi-node/src/javaRestTest/java/org/elasticsearch/xpack/TimeSeriesRestDriver.java
@@ -455,6 +455,9 @@ public static String waitAndGetShrinkIndexName(RestClient client, String origina
                     "GET",
                     SHRUNKEN_INDEX_PREFIX + "*" + originalIndex + "," + originalIndex + "/_ilm/explain"
                 );
+                // Sometimes, the original index might already have been deleted, so we need to ignore unavailable (concrete) indices.
+                explainRequest.addParameter("ignore_unavailable", Boolean.toString(true));
+                explainRequest.addParameter("expand_wildcards", "open,hidden");
                 explainRequest.addParameter("only_errors", Boolean.toString(false));
                 explainRequest.addParameter("only_managed", Boolean.toString(false));
                 Response response = client.performRequest(explainRequest);
diff --git a/x-pack/plugin/ilm/qa/multi-node/src/javaRestTest/java/org/elasticsearch/xpack/ilm/TimeSeriesDataStreamsIT.java b/x-pack/plugin/ilm/qa/multi-node/src/javaRestTest/java/org/elasticsearch/xpack/ilm/TimeSeriesDataStreamsIT.java
index cf55fc0e0ac5a..1faf29b64fc4a 100644
--- a/x-pack/plugin/ilm/qa/multi-node/src/javaRestTest/java/org/elasticsearch/xpack/ilm/TimeSeriesDataStreamsIT.java
+++ b/x-pack/plugin/ilm/qa/multi-node/src/javaRestTest/java/org/elasticsearch/xpack/ilm/TimeSeriesDataStreamsIT.java
@@ -120,7 +120,6 @@ public void testRolloverIsSkippedOnManualDataStreamRollover() throws Exception {
         );
     }
 
-    @AwaitsFix(bugUrl = "https://github.com/elastic/elasticsearch/issues/70595")
     public void testShrinkActionInPolicyWithoutHotPhase() throws Exception {
         createNewSingletonPolicy(client(), policyName, "warm", new ShrinkAction(1, null, false));
         createComposableTemplate(client(), template, dataStream + "*", getTemplate(policyName));