diff --git a/alerts/apps_alerts.libsonnet b/alerts/apps_alerts.libsonnet
index 46363745d..5d2d8f373 100644
--- a/alerts/apps_alerts.libsonnet
+++ b/alerts/apps_alerts.libsonnet
@@ -167,13 +167,13 @@ local utils = import '../lib/utils.libsonnet';
                     unless
                   kube_statefulset_status_update_revision{%(prefixedNamespaceSelector)s%(kubeStateMetricsSelector)s}
                 )
-                  *
+                  * on(namespace, statefulset, job, %(clusterLabel)s)
                 (
                   kube_statefulset_replicas{%(prefixedNamespaceSelector)s%(kubeStateMetricsSelector)s}
                     !=
                   kube_statefulset_status_replicas_updated{%(prefixedNamespaceSelector)s%(kubeStateMetricsSelector)s}
                 )
-              )  and (
+              )  and on(namespace, statefulset, job, %(clusterLabel)s) (
                 changes(kube_statefulset_status_replicas_updated{%(prefixedNamespaceSelector)s%(kubeStateMetricsSelector)s}[5m])
                   ==
                 0
diff --git a/tests/apps_alerts-test.yaml b/tests/apps_alerts-test.yaml
index 803c61944..3ab42d042 100644
--- a/tests/apps_alerts-test.yaml
+++ b/tests/apps_alerts-test.yaml
@@ -25,3 +25,31 @@ tests:
         description: "PDB ns1/pdb1 expects 1 more healthy pods. The desired number of healthy pods has not been met for at least 15m."
         runbook_url: "https://github.com/kubernetes-monitoring/kubernetes-mixin/tree/master/runbook.md#alert-name-kubepdbnotenoughhealthypods"
         summary: "PDB does not have enough healthy pods."
+
+- interval: 1m
+  name: KubeStatefulSetUpdateNotRolledOut still fires even if another label (e.g. instance) is present
+  input_series:
+  - series: 'kube_statefulset_status_current_revision{job="kube-state-metrics", cluster="c1", namespace="ns1", statefulset="ss1", revision="foo", instance="custom"}'
+    values: '1x15'
+  - series: 'kube_statefulset_status_update_revision{job="kube-state-metrics", cluster="c1", namespace="ns1", statefulset="ss1", revision="bar", instance="custom"}'
+    values: '1x15'
+  - series: 'kube_statefulset_replicas{job="kube-state-metrics", cluster="c1", namespace="ns1", statefulset="ss1", instance="custom"}'
+    values: '5x15'
+  - series: 'kube_statefulset_status_replicas_updated{job="kube-state-metrics", cluster="c1", namespace="ns1", statefulset="ss1", instance="custom"}'
+    values: '1x15'
+  alert_rule_test:
+  - eval_time: 14m
+    alertname: KubeStatefulSetUpdateNotRolledOut
+  - eval_time: 15m
+    alertname: KubeStatefulSetUpdateNotRolledOut
+    exp_alerts:
+    - exp_labels:
+        cluster: "c1"
+        job: "kube-state-metrics"
+        namespace: "ns1"
+        severity: "warning"
+        statefulset: "ss1"
+      exp_annotations:
+        description: "StatefulSet ns1/ss1 update has not been rolled out."
+        runbook_url: "https://github.com/kubernetes-monitoring/kubernetes-mixin/tree/master/runbook.md#alert-name-kubestatefulsetupdatenotrolledout"
+        summary: "StatefulSet update has not been rolled out."