diff --git a/docs/reference/operator_parameters.md b/docs/reference/operator_parameters.md
index 9d4e5fc58..a812c5d9f 100644
--- a/docs/reference/operator_parameters.md
+++ b/docs/reference/operator_parameters.md
@@ -273,9 +273,9 @@ configuration they are grouped under the `kubernetes` key.
 
 * **inherited_annotations**
   list of annotation keys that can be inherited from the cluster manifest, and
-  added to each child objects  (`Deployment`, `StatefulSet`, `Pod`, `PVCs`,
-  `PDB`, `Service`, `Endpoints` and `Secrets`) created by the operator.
-  The default is empty.
+  added to each child objects  (`Deployment`, `StatefulSet`, `Pod`, `PDB` and
+  `Services`) created by the operator incl. the ones from the connection
+  pooler deployment. The default is empty.
 
 * **pod_role_label**
   name of the label assigned to the Postgres pods (and services/endpoints) by
diff --git a/pkg/cluster/connection_pooler.go b/pkg/cluster/connection_pooler.go
index 53c036287..d36aff7f1 100644
--- a/pkg/cluster/connection_pooler.go
+++ b/pkg/cluster/connection_pooler.go
@@ -334,15 +334,12 @@ func (c *Cluster) generateConnectionPoolerDeployment(connectionPooler *Connectio
 		return nil, err
 	}
 
-	annotations := c.annotationsSet(nil)
-	annotations = c.AnnotationsToPropagate(annotations)
-
 	deployment := &appsv1.Deployment{
 		ObjectMeta: metav1.ObjectMeta{
 			Name:        connectionPooler.Name,
 			Namespace:   connectionPooler.Namespace,
 			Labels:      c.connectionPoolerLabels(connectionPooler.Role, true).MatchLabels,
-			Annotations: annotations,
+			Annotations: c.AnnotationsToPropagate(c.annotationsSet(nil)),
 			// make StatefulSet object its owner to represent the dependency.
 			// By itself StatefulSet is being deleted with "Orphaned"
 			// propagation policy, which means that it's deletion will not
@@ -869,8 +866,7 @@ func (c *Cluster) syncConnectionPoolerWorker(oldSpec, newSpec *acidv1.Postgresql
 		}
 	}
 
-	newAnnotations := c.annotationsSet(c.ConnectionPooler[role].Deployment.Annotations)
-	newAnnotations = c.AnnotationsToPropagate(newAnnotations)
+	newAnnotations := c.AnnotationsToPropagate(c.annotationsSet(c.ConnectionPooler[role].Deployment.Annotations))
 	if newAnnotations != nil && len(newAnnotations) > 0 {
 		deployment, err = updateConnectionPoolerAnnotations(c.KubeClient, c.ConnectionPooler[role].Deployment, newAnnotations)
 		if err != nil {
diff --git a/pkg/cluster/k8sres.go b/pkg/cluster/k8sres.go
index b5b842053..a585649db 100644
--- a/pkg/cluster/k8sres.go
+++ b/pkg/cluster/k8sres.go
@@ -1226,9 +1226,9 @@ func (c *Cluster) generateStatefulSet(spec *acidv1.PostgresSpec) (*appsv1.Statef
 		return nil, fmt.Errorf("could not set the pod management policy to the unknown value: %v", c.OpConfig.PodManagementPolicy)
 	}
 
-	stsAnnotations := c.annotationsSet(nil)
-	stsAnnotations = c.AnnotationsToPropagate(stsAnnotations)
+	stsAnnotations := make(map[string]string)
 	stsAnnotations[rollingUpdateStatefulsetAnnotationKey] = strconv.FormatBool(false)
+	stsAnnotations = c.AnnotationsToPropagate(c.annotationsSet(nil))
 
 	statefulSet := &appsv1.StatefulSet{
 		ObjectMeta: metav1.ObjectMeta{
diff --git a/pkg/cluster/sync.go b/pkg/cluster/sync.go
index 997d6db19..211903689 100644
--- a/pkg/cluster/sync.go
+++ b/pkg/cluster/sync.go
@@ -353,9 +353,8 @@ func (c *Cluster) syncStatefulSet() error {
 				}
 			}
 		}
-		annotations := c.annotationsSet(c.Statefulset.Annotations)
-		annotations = c.AnnotationsToPropagate(annotations)
-		c.updateStatefulSetAnnotations(annotations)
+
+		c.updateStatefulSetAnnotations(c.AnnotationsToPropagate(c.annotationsSet(c.Statefulset.Annotations)))
 
 		if !podsRollingUpdateRequired && !c.OpConfig.EnableLazySpiloUpgrade {
 			// even if desired and actual statefulsets match
@@ -420,7 +419,11 @@ func (c *Cluster) AnnotationsToPropagate(annotations map[string]string) map[stri
 		}
 	}
 
-	return annotations
+	if len(annotations) > 0 {
+		return annotations
+	}
+
+	return nil
 }
 
 // checkAndSetGlobalPostgreSQLConfiguration checks whether cluster-wide API parameters