diff --git a/test/integration/objectstore/_purged_handling.py b/test/integration/objectstore/_purged_handling.py
index 1437f6742ae5..097a9f922360 100644
--- a/test/integration/objectstore/_purged_handling.py
+++ b/test/integration/objectstore/_purged_handling.py
@@ -9,7 +9,7 @@ def purge_while_job_running(dataset_populator: DatasetPopulator, extra_sleep=0):
         response = dataset_populator.run_tool(
             "all_output_types",
             inputs={
-                "sleep_param": 5,
+                "sleep_param": 5 + extra_sleep,
             },
             history_id=history_id,
         )
diff --git a/test/integration/test_extended_metadata.py b/test/integration/test_extended_metadata.py
index d267ed01c418..50c21940cfba 100644
--- a/test/integration/test_extended_metadata.py
+++ b/test/integration/test_extended_metadata.py
@@ -100,7 +100,7 @@ def test_fetch_data_library(self):
     def test_purge_while_job_running(self):
         # pass extra_sleep, since templating the command line will fail if the output
         # is deleted before remote_tool_eval runs.
-        purge_while_job_running(self.dataset_populator, extra_sleep=4)
+        purge_while_job_running(self.dataset_populator, extra_sleep=10)
 
 
 class TestExtendedMetadataDeferredIntegration(integration_util.IntegrationTestCase):