diff --git a/GNUmakefile b/GNUmakefile
index 408d8891e08..bafced17bbb 100644
--- a/GNUmakefile
+++ b/GNUmakefile
@@ -1,4 +1,4 @@
-SWEEP?=us-east-1,us-east-2,us-west-2
+SWEEP?=us-west-2,us-east-1,us-east-2
 TEST?=./...
 SWEEP_DIR?=./internal/sweep
 PKG_NAME=internal
@@ -16,6 +16,7 @@ gen:
 	go generate ./...
 
 sweep:
+	# make sweep SWEEPARGS=-sweep-run=aws_example_thing
 	@echo "WARNING: This will destroy infrastructure. Use only in development accounts."
 	go test $(SWEEP_DIR) -v -tags=sweep -sweep=$(SWEEP) $(SWEEPARGS) -timeout 60m
 
diff --git a/internal/service/dms/sweep.go b/internal/service/dms/sweep.go
index 967cf780646..b81f4f8a899 100644
--- a/internal/service/dms/sweep.go
+++ b/internal/service/dms/sweep.go
@@ -19,6 +19,14 @@ func init() {
 	resource.AddTestSweepers("aws_dms_replication_instance", &resource.Sweeper{
 		Name: "aws_dms_replication_instance",
 		F:    sweepReplicationInstances,
+		Dependencies: []string{
+			"aws_dms_replication_task",
+		},
+	})
+
+	resource.AddTestSweepers("aws_dms_replication_task", &resource.Sweeper{
+		Name: "aws_dms_replication_task",
+		F:    sweepReplicationTasks,
 	})
 }
 
@@ -61,3 +69,46 @@ func sweepReplicationInstances(region string) error {
 
 	return errs.ErrorOrNil()
 }
+
+func sweepReplicationTasks(region string) error {
+	client, err := sweep.SharedRegionalSweepClient(region)
+
+	if err != nil {
+		return fmt.Errorf("error getting client: %s", err)
+	}
+
+	conn := client.(*conns.AWSClient).DMSConn
+	sweepResources := make([]*sweep.SweepResource, 0)
+	var errs *multierror.Error
+
+	input := &dms.DescribeReplicationTasksInput{
+		WithoutSettings: aws.Bool(true),
+	}
+	err = conn.DescribeReplicationTasksPages(input, func(page *dms.DescribeReplicationTasksOutput, lastPage bool) bool {
+		for _, instance := range page.ReplicationTasks {
+			r := ResourceReplicationTask()
+			d := r.Data(nil)
+			d.SetId(aws.StringValue(instance.ReplicationTaskIdentifier))
+			d.Set("replication_task_arn", instance.ReplicationTaskArn)
+
+			sweepResources = append(sweepResources, sweep.NewSweepResource(r, d, client))
+		}
+
+		return !lastPage
+	})
+
+	if err != nil {
+		errs = multierror.Append(errs, fmt.Errorf("error describing DMS Replication Tasks: %w", err))
+	}
+
+	if err = sweep.SweepOrchestrator(sweepResources); err != nil {
+		errs = multierror.Append(errs, fmt.Errorf("error sweeping DMS Replication Tasks for %s: %w", region, err))
+	}
+
+	if sweep.SkipSweepError(errs.ErrorOrNil()) {
+		log.Printf("[WARN] Skipping DMS Replication Instance sweep for %s: %s", region, err)
+		return nil
+	}
+
+	return errs.ErrorOrNil()
+}
diff --git a/internal/service/ec2/sweep.go b/internal/service/ec2/sweep.go
index c9168ffc501..a19910a6565 100644
--- a/internal/service/ec2/sweep.go
+++ b/internal/service/ec2/sweep.go
@@ -170,6 +170,7 @@ func init() {
 			"aws_cloudhsm_v2_cluster",
 			"aws_db_subnet_group",
 			"aws_directory_service_directory",
+			"aws_dms_replication_instance",
 			"aws_ec2_client_vpn_endpoint",
 			"aws_ec2_transit_gateway_vpc_attachment",
 			"aws_efs_file_system",