diff --git a/newsfragments/598.internal.md b/newsfragments/598.internal.md
new file mode 100644
index 000000000..431cc1cd8
--- /dev/null
+++ b/newsfragments/598.internal.md
@@ -0,0 +1 @@
+Tests: don't check services matching labels against terminating pods.
diff --git a/tests/integration/test_networking.py b/tests/integration/test_networking.py
index 2e501bbc3..e8ea68f9b 100644
--- a/tests/integration/test_networking.py
+++ b/tests/integration/test_networking.py
@@ -40,7 +40,7 @@ async def test_services_have_matching_labels(
         label_selectors = {label: value for label, value in service.spec.selector.items()}
 
         async for pod in kube_client.list(Pod, namespace=generated_data.ess_namespace, labels=label_selectors):
-            if pod.status and pod.status.phase == "Terminating":
+            if pod.status and pod.status.phase not in ("Terminating", "Succeeded"):
                 continue  # Skip terminating pods
             assert service.metadata, f"Encountered a service without metadata : {service}"
             assert pod.metadata, f"Encountered a pod without metadata : {pod}"
@@ -58,7 +58,10 @@ async def test_services_have_matching_labels(
                 assert value.startswith(
                     pod.metadata.labels[label.replace("k8s.element.io/target-", "app.kubernetes.io/")]
                 ), (
-                    f"{pod.metadata.name} does not have the correct label {label}={value} "
+                    f"Service/{service.metadata.name} has {label=}={value=} "
+                    f"which does not start with the value from the Pod/{pod.metadata.name} "
+                    f"{label.replace('k8s.element.io/target-', 'app.kubernetes.io/')}="
+                    f"{pod.metadata.labels[label.replace('k8s.element.io/target-', 'app.kubernetes.io/')]} "
                     f"(pod status phase : {pod.status.phase if pod.status else 'N/A'}"
                 )