diff --git a/scheduler/generic_sched_test.go b/scheduler/generic_sched_test.go
index e3d5e9a84..43853fd2e 100644
--- a/scheduler/generic_sched_test.go
+++ b/scheduler/generic_sched_test.go
@@ -1316,3 +1316,71 @@ func TestBatchSched_Run_FailedAlloc(t *testing.T) {
 
 	h.AssertEvalStatus(t, structs.EvalStatusComplete)
 }
+
+func TestBatchSched_ReRun_SuccessfullyFinishedAlloc(t *testing.T) {
+	h := NewHarness(t)
+
+	// Create two nodes, one that is drained and has a successfully finished
+	// alloc and a fresh undrained one
+	node := mock.Node()
+	node.Drain = true
+	node2 := mock.Node()
+	noErr(t, h.State.UpsertNode(h.NextIndex(), node))
+	noErr(t, h.State.UpsertNode(h.NextIndex(), node2))
+
+	// Create a job
+	job := mock.Job()
+	job.Type = structs.JobTypeBatch
+	job.TaskGroups[0].Count = 1
+	noErr(t, h.State.UpsertJob(h.NextIndex(), job))
+
+	// Create a successful alloc
+	alloc := mock.Alloc()
+	alloc.Job = job
+	alloc.JobID = job.ID
+	alloc.NodeID = node.ID
+	alloc.Name = "my-job.web[0]"
+	alloc.ClientStatus = structs.AllocClientStatusComplete
+	alloc.TaskStates = map[string]*structs.TaskState{
+		"web": &structs.TaskState{
+			State: structs.TaskStateDead,
+			Events: []*structs.TaskEvent{
+				{
+					Type:     structs.TaskTerminated,
+					ExitCode: 0,
+				},
+			},
+		},
+	}
+	noErr(t, h.State.UpsertAllocs(h.NextIndex(), []*structs.Allocation{alloc}))
+
+	// Create a mock evaluation to rerun the job
+	eval := &structs.Evaluation{
+		ID:          structs.GenerateUUID(),
+		Priority:    job.Priority,
+		TriggeredBy: structs.EvalTriggerJobRegister,
+		JobID:       job.ID,
+	}
+
+	// Process the evaluation
+	err := h.Process(NewBatchScheduler, eval)
+	if err != nil {
+		t.Fatalf("err: %v", err)
+	}
+
+	// Ensure no plan
+	if len(h.Plans) != 0 {
+		t.Fatalf("bad: %#v", h.Plans)
+	}
+
+	// Lookup the allocations by JobID
+	out, err := h.State.AllocsByJob(job.ID)
+	noErr(t, err)
+
+	// Ensure no replacement alloc was placed.
+	if len(out) != 1 {
+		t.Fatalf("bad: %#v", out)
+	}
+
+	h.AssertEvalStatus(t, structs.EvalStatusComplete)
+}
diff --git a/scheduler/util.go b/scheduler/util.go
index 9c3035ee4..e910f3db1 100644
--- a/scheduler/util.go
+++ b/scheduler/util.go
@@ -84,13 +84,14 @@ func diffAllocs(job *structs.Job, taintedNodes map[string]bool,
 		// If we are on a tainted node, we must migrate if we are a service or
 		// if the batch allocation did not finish
 		if taintedNodes[exist.NodeID] {
-			if exist.Job.Type != structs.JobTypeBatch || !exist.RanSuccessfully() {
-				result.migrate = append(result.migrate, allocTuple{
-					Name:      name,
-					TaskGroup: tg,
-					Alloc:     exist,
-				})
+			if exist.Job.Type == structs.JobTypeBatch && exist.RanSuccessfully() {
+				goto IGNORE
 			}
+			result.migrate = append(result.migrate, allocTuple{
+				Name:      name,
+				TaskGroup: tg,
+				Alloc:     exist,
+			})
 			continue
 		}
 
@@ -105,6 +106,7 @@ func diffAllocs(job *structs.Job, taintedNodes map[string]bool,
 		}
 
 		// Everything is up-to-date
+	IGNORE:
 		result.ignore = append(result.ignore, allocTuple{
 			Name:      name,
 			TaskGroup: tg,
diff --git a/scheduler/util_test.go b/scheduler/util_test.go
index 1d689fe2b..57e2cb482 100644
--- a/scheduler/util_test.go
+++ b/scheduler/util_test.go
@@ -74,6 +74,7 @@ func TestDiffAllocs(t *testing.T) {
 			ID:     structs.GenerateUUID(),
 			NodeID: "zip",
 			Name:   "my-job.web[10]",
+			Job:    oldJob,
 		},
 
 		// Migrate the 3rd
@@ -81,6 +82,7 @@ func TestDiffAllocs(t *testing.T) {
 			ID:     structs.GenerateUUID(),
 			NodeID: "dead",
 			Name:   "my-job.web[2]",
+			Job:    oldJob,
 		},
 	}
 
@@ -155,6 +157,7 @@ func TestDiffSystemAllocs(t *testing.T) {
 			ID:     structs.GenerateUUID(),
 			NodeID: "dead",
 			Name:   "my-job.web[0]",
+			Job:    oldJob,
 		},
 	}