diff --git a/muted-tests.yml b/muted-tests.yml
index 81672399a056d..ea5f2dfbd44ed 100644
--- a/muted-tests.yml
+++ b/muted-tests.yml
@@ -303,12 +303,6 @@ tests:
 - class: org.elasticsearch.xpack.inference.integration.AuthorizationTaskExecutorMultipleNodesIT
   method: testAuthorizationTaskGetsRelocatedToAnotherNode_WhenTheNodeThatIsRunningItShutsDown
   issue: https://github.com/elastic/elasticsearch/issues/137911
-- class: org.elasticsearch.repositories.blobstore.testkit.rest.SnapshotRepoTestKitClientYamlTestSuiteIT
-  method: test {p0=/10_analyze/Analysis without details}
-  issue: https://github.com/elastic/elasticsearch/issues/140627
-- class: org.elasticsearch.repositories.blobstore.testkit.analyze.RepositoryAnalysisSuccessIT
-  method: testRepositoryAnalysis
-  issue: https://github.com/elastic/elasticsearch/issues/140638
 - class: org.elasticsearch.xpack.esql.qa.single_node.EsqlSpecIT
   method: test {csv-spec:string.Url_encode_component tests with table reads}
   issue: https://github.com/elastic/elasticsearch/issues/140621
@@ -339,9 +333,6 @@ tests:
 - class: org.elasticsearch.xpack.esql.qa.single_node.GenerativeForkIT
   method: test {csv-spec:string.Url_encode_component tests with table reads}
   issue: https://github.com/elastic/elasticsearch/issues/140809
-- class: org.elasticsearch.repositories.blobstore.testkit.analyze.RepositoryAnalysisFailureIT
-  method: testFailsOnCopyAfterWrite
-  issue: https://github.com/elastic/elasticsearch/issues/140819
 - class: org.elasticsearch.xpack.inference.services.jinaai.JinaAIServiceTests
   method: test_embeddingModel_chunkedInfer_batchesCallsWhenLateChunkingEnabled
   issue: https://github.com/elastic/elasticsearch/issues/140890
diff --git a/x-pack/plugin/snapshot-repo-test-kit/qa/rest/src/yamlRestTest/resources/rest-api-spec/test/10_analyze.yml b/x-pack/plugin/snapshot-repo-test-kit/qa/rest/src/yamlRestTest/resources/rest-api-spec/test/10_analyze.yml
index bcee1691e033c..66801ebb2c9a5 100644
--- a/x-pack/plugin/snapshot-repo-test-kit/qa/rest/src/yamlRestTest/resources/rest-api-spec/test/10_analyze.yml
+++ b/x-pack/plugin/snapshot-repo-test-kit/qa/rest/src/yamlRestTest/resources/rest-api-spec/test/10_analyze.yml
@@ -86,7 +86,11 @@ setup:
   - is_true: summary.write.total_throttled
   - gte: { summary.write.total_elapsed_nanos: 0}
   - is_true: summary.write.total_elapsed
-  - gte: { summary.read.count: 10}
+
+  # extraordinarily unlikely but in theory up to half of the writes could be copies, and each of those writes could
+  # attempt the copy early, fail with a NoSuchFileException, and thus not attempt to read the copy, so we can only
+  # assert this:
+  - gte: { summary.read.count: 5}
   - gte: { summary.read.total_size_bytes: 0}
   - is_true: summary.read.total_size
   - gte: { summary.read.total_wait_nanos: 0}
diff --git a/x-pack/plugin/snapshot-repo-test-kit/src/internalClusterTest/java/org/elasticsearch/repositories/blobstore/testkit/analyze/RepositoryAnalysisSuccessIT.java b/x-pack/plugin/snapshot-repo-test-kit/src/internalClusterTest/java/org/elasticsearch/repositories/blobstore/testkit/analyze/RepositoryAnalysisSuccessIT.java
index 5ffd6883eabb6..a227684ad938d 100644
--- a/x-pack/plugin/snapshot-repo-test-kit/src/internalClusterTest/java/org/elasticsearch/repositories/blobstore/testkit/analyze/RepositoryAnalysisSuccessIT.java
+++ b/x-pack/plugin/snapshot-repo-test-kit/src/internalClusterTest/java/org/elasticsearch/repositories/blobstore/testkit/analyze/RepositoryAnalysisSuccessIT.java
@@ -170,7 +170,12 @@ static void assertResponseSummaryFields(RepositoryAnalyzeAction.Request request,
             final var responseMap = convertToMap(response);
             final var responseString = Strings.toString(response);
             assertThat(responseString, ObjectPath.eval("summary.write.count", responseMap), equalTo(request.getBlobCount()));
-            assertThat(responseString, ObjectPath.eval("summary.read.count", responseMap), greaterThanOrEqualTo(request.getBlobCount()));
+
+            // extraordinarily unlikely but in theory up to half of the writes could be copies, and each of those writes could attempt the
+            // copy early, fail with a NoSuchFileException, and thus not attempt to read the copy, so we can only assert this:
+            final var minReadCount = request.getBlobCount() / 2;
+            assertThat(responseString, ObjectPath.eval("summary.read.count", responseMap), greaterThanOrEqualTo(minReadCount));
+
             assertThat(responseString, ObjectPath.eval("summary.write.total_throttled_nanos", responseMap), equalTo(0));
             assertThat(responseString, ObjectPath.eval("summary.read.total_throttled_nanos", responseMap), equalTo(0));
         } catch (IOException e) {