diff --git a/manager/orchestrator/constraintenforcer/constraint_enforcer.go b/manager/orchestrator/constraintenforcer/constraint_enforcer.go
index 296767852e..12fa40151f 100644
--- a/manager/orchestrator/constraintenforcer/constraint_enforcer.go
+++ b/manager/orchestrator/constraintenforcer/constraint_enforcer.go
@@ -118,6 +118,12 @@ loop:
 		if t.DesiredState < api.TaskStateAssigned || t.DesiredState > api.TaskStateCompleted {
 			continue
 		}
+		// Completed tasks should not consume node reservations. This is
+		// particularly important for replicated-job services, where tasks may
+		// remain with DesiredState=Completed after they finished.
+		if t.Status.State >= api.TaskStateCompleted {
+			continue
+		}
 
 		// Ensure that the node still satisfies placement constraints.
 		// NOTE: If the task is associacted with a service then we must use the
diff --git a/manager/orchestrator/constraintenforcer/constraint_enforcer_test.go b/manager/orchestrator/constraintenforcer/constraint_enforcer_test.go
index f63518b1aa..527af9d1d9 100644
--- a/manager/orchestrator/constraintenforcer/constraint_enforcer_test.go
+++ b/manager/orchestrator/constraintenforcer/constraint_enforcer_test.go
@@ -12,6 +12,82 @@ import (
 	"github.com/stretchr/testify/require"
 )
 
+func TestRejectNoncompliantTasksIgnoresCompletedJobTasksInReservations(t *testing.T) {
+	s := store.NewMemoryStore(nil)
+	require.NotNil(t, s)
+	t.Cleanup(func() { _ = s.Close() })
+
+	node := &api.Node{
+		ID: "node1",
+		Spec: api.NodeSpec{
+			Availability: api.NodeAvailabilityActive,
+		},
+		Description: &api.NodeDescription{
+			Resources: &api.Resources{
+				MemoryBytes: 1024,
+			},
+		},
+	}
+
+	// A live task that fits if completed job tasks are ignored.
+	runningTask := &api.Task{
+		ID:           "running1",
+		NodeID:       node.ID,
+		ServiceID:    "svc1",
+		DesiredState: api.TaskStateRunning,
+		Status: api.TaskStatus{
+			State: api.TaskStateRunning,
+		},
+		Spec: api.TaskSpec{
+			Resources: &api.ResourceRequirements{
+				Reservations: &api.Resources{
+					MemoryBytes: 700,
+				},
+			},
+		},
+	}
+
+	// A completed replicated-job task that should not consume reservations.
+	completedJobTask := &api.Task{
+		ID:           "job1",
+		NodeID:       node.ID,
+		ServiceID:    "jobsvc",
+		DesiredState: api.TaskStateCompleted,
+		Status: api.TaskStatus{
+			State: api.TaskStateCompleted,
+		},
+		Spec: api.TaskSpec{
+			Resources: &api.ResourceRequirements{
+				Reservations: &api.Resources{
+					MemoryBytes: 700,
+				},
+			},
+		},
+	}
+
+	require.NoError(t, s.Update(func(tx store.Tx) error {
+		if err := store.CreateNode(tx, node); err != nil {
+			return err
+		}
+		if err := store.CreateTask(tx, runningTask); err != nil {
+			return err
+		}
+		if err := store.CreateTask(tx, completedJobTask); err != nil {
+			return err
+		}
+		return nil
+	}))
+
+	ce := New(s)
+	ce.rejectNoncompliantTasks(node)
+
+	s.View(func(tx store.ReadTx) {
+		got := store.GetTask(tx, runningTask.ID)
+		require.NotNil(t, got)
+		assert.NotEqual(t, api.TaskStateRejected, got.Status.State, "running task unexpectedly rejected; completed job tasks should not count toward reservations")
+	})
+}
+
 func TestConstraintEnforcer(t *testing.T) {
 	nodes := []*api.Node{
 		// this node starts as a worker, but then is changed to a manager.