diff --git a/.changelog/34187.txt b/.changelog/34187.txt
new file mode 100644
index 000000000000..b3c62485409a
--- /dev/null
+++ b/.changelog/34187.txt
@@ -0,0 +1,7 @@
+```release-note:enhancement
+resource/aws_rds_cluster: Remove the provider default (previously, "1") and use the AWS default for `backup_retention_period` (also, "1") to allow integration with AWS Backup
+```
+
+```release-note:bug
+resource/aws_rds_cluster: Avoid an error on delete related to `unexpected state 'scaling-compute'`
+```
\ No newline at end of file
diff --git a/internal/service/rds/cluster.go b/internal/service/rds/cluster.go
index 135601af2498..51c5db656a41 100644
--- a/internal/service/rds/cluster.go
+++ b/internal/service/rds/cluster.go
@@ -87,7 +87,7 @@ func ResourceCluster() *schema.Resource {
 			"backup_retention_period": {
 				Type:         schema.TypeInt,
 				Optional:     true,
-				Default:      1,
+				Computed:     true,
 				ValidateFunc: validation.IntAtMost(35),
 			},
 			"backtrack_window": {
@@ -1740,6 +1740,7 @@ func waitDBClusterDeleted(ctx context.Context, conn *rds.RDS, id string, timeout
 			ClusterStatusDeleting,
 			ClusterStatusModifying,
 			ClusterStatusPromoting,
+			ClusterStatusScalingCompute,
 		},
 		Target:     []string{},
 		Refresh:    statusDBCluster(ctx, conn, id),