diff --git a/internal/rdb/rdb.go b/internal/rdb/rdb.go
index 6b916f0..36a407e 100644
--- a/internal/rdb/rdb.go
+++ b/internal/rdb/rdb.go
@@ -918,10 +918,10 @@ func (r *RDB) deleteExpiredCompletedTasks(qname string, batchSize int) (int64, e
 	return n, nil
 }
 
-// KEYS[1] -> asynq:{<qname>}:deadlines
-// ARGV[1] -> deadline in unix time
+// KEYS[1] -> asynq:{<qname>}:lease
+// ARGV[1] -> cutoff in unix time
 // ARGV[2] -> task key prefix
-var listDeadlineExceededCmd = redis.NewScript(`
+var listLeaseExpiredCmd = redis.NewScript(`
 local res = {}
 local ids = redis.call("ZRANGEBYSCORE", KEYS[1], "-inf", ARGV[1])
 for _, id in ipairs(ids) do
@@ -931,14 +931,14 @@ end
 return res
 `)
 
-// ListDeadlineExceeded returns a list of task messages that have exceeded the deadline from the given queues.
-func (r *RDB) ListDeadlineExceeded(deadline time.Time, qnames ...string) ([]*base.TaskMessage, error) {
-	var op errors.Op = "rdb.ListDeadlineExceeded"
+// ListLeaseExpired returns a list of task messages with an expired lease from the given queues.
+func (r *RDB) ListLeaseExpired(cutoff time.Time, qnames ...string) ([]*base.TaskMessage, error) {
+	var op errors.Op = "rdb.ListLeaseExpired"
 	var msgs []*base.TaskMessage
 	for _, qname := range qnames {
-		res, err := listDeadlineExceededCmd.Run(context.Background(), r.client,
-			[]string{base.DeadlinesKey(qname)},
-			deadline.Unix(), base.TaskKeyPrefix(qname)).Result()
+		res, err := listLeaseExpiredCmd.Run(context.Background(), r.client,
+			[]string{base.LeaseKey(qname)},
+			cutoff.Unix(), base.TaskKeyPrefix(qname)).Result()
 		if err != nil {
 			return nil, errors.E(op, errors.Internal, fmt.Sprintf("redis eval error: %v", err))
 		}
diff --git a/internal/rdb/rdb_test.go b/internal/rdb/rdb_test.go
index a2e479e..5f32012 100644
--- a/internal/rdb/rdb_test.go
+++ b/internal/rdb/rdb_test.go
@@ -2208,71 +2208,67 @@ func TestDeleteExpiredCompletedTasks(t *testing.T) {
 	}
 }
 
-func TestListDeadlineExceeded(t *testing.T) {
+func TestListLeaseExpired(t *testing.T) {
 	t1 := h.NewTaskMessageWithQueue("task1", nil, "default")
 	t2 := h.NewTaskMessageWithQueue("task2", nil, "default")
 	t3 := h.NewTaskMessageWithQueue("task3", nil, "critical")
 
 	now := time.Now()
-	oneHourFromNow := now.Add(1 * time.Hour)
-	fiveMinutesFromNow := now.Add(5 * time.Minute)
-	fiveMinutesAgo := now.Add(-5 * time.Minute)
-	oneHourAgo := now.Add(-1 * time.Hour)
 
 	tests := []struct {
-		desc      string
-		deadlines map[string][]base.Z
-		qnames    []string
-		t         time.Time
-		want      []*base.TaskMessage
+		desc   string
+		lease  map[string][]base.Z
+		qnames []string
+		cutoff time.Time
+		want   []*base.TaskMessage
 	}{
 		{
 			desc: "with a single active task",
-			deadlines: map[string][]base.Z{
-				"default": {{Message: t1, Score: fiveMinutesAgo.Unix()}},
+			lease: map[string][]base.Z{
+				"default": {{Message: t1, Score: now.Add(-10 * time.Second).Unix()}},
 			},
 			qnames: []string{"default"},
-			t:      time.Now(),
+			cutoff: now,
 			want:   []*base.TaskMessage{t1},
 		},
 		{
 			desc: "with multiple active tasks, and one expired",
-			deadlines: map[string][]base.Z{
+			lease: map[string][]base.Z{
 				"default": {
-					{Message: t1, Score: oneHourAgo.Unix()},
-					{Message: t2, Score: fiveMinutesFromNow.Unix()},
+					{Message: t1, Score: now.Add(-5 * time.Minute).Unix()},
+					{Message: t2, Score: now.Add(20 * time.Second).Unix()},
 				},
 				"critical": {
-					{Message: t3, Score: oneHourFromNow.Unix()},
+					{Message: t3, Score: now.Add(10 * time.Second).Unix()},
 				},
 			},
 			qnames: []string{"default", "critical"},
-			t:      time.Now(),
+			cutoff: now,
 			want:   []*base.TaskMessage{t1},
 		},
 		{
 			desc: "with multiple expired active tasks",
-			deadlines: map[string][]base.Z{
+			lease: map[string][]base.Z{
 				"default": {
-					{Message: t1, Score: oneHourAgo.Unix()},
-					{Message: t2, Score: oneHourFromNow.Unix()},
+					{Message: t1, Score: now.Add(-2 * time.Minute).Unix()},
+					{Message: t2, Score: now.Add(20 * time.Second).Unix()},
 				},
 				"critical": {
-					{Message: t3, Score: fiveMinutesAgo.Unix()},
+					{Message: t3, Score: now.Add(-30 * time.Second).Unix()},
 				},
 			},
 			qnames: []string{"default", "critical"},
-			t:      time.Now(),
+			cutoff: now,
 			want:   []*base.TaskMessage{t1, t3},
 		},
 		{
 			desc: "with empty active queue",
-			deadlines: map[string][]base.Z{
+			lease: map[string][]base.Z{
 				"default":  {},
 				"critical": {},
 			},
 			qnames: []string{"default", "critical"},
-			t:      time.Now(),
+			cutoff: now,
 			want:   []*base.TaskMessage{},
 		},
 	}
@@ -2281,17 +2277,17 @@ func TestListDeadlineExceeded(t *testing.T) {
 	defer r.Close()
 	for _, tc := range tests {
 		h.FlushDB(t, r.client)
-		h.SeedAllLease(t, r.client, tc.deadlines)
+		h.SeedAllLease(t, r.client, tc.lease)
 
-		got, err := r.ListDeadlineExceeded(tc.t, tc.qnames...)
+		got, err := r.ListLeaseExpired(tc.cutoff, tc.qnames...)
 		if err != nil {
-			t.Errorf("%s; ListDeadlineExceeded(%v) returned error: %v", tc.desc, tc.t, err)
+			t.Errorf("%s; ListLeaseExpired(%v) returned error: %v", tc.desc, tc.cutoff, err)
 			continue
 		}
 
 		if diff := cmp.Diff(tc.want, got, h.SortMsgOpt); diff != "" {
-			t.Errorf("%s; ListDeadlineExceeded(%v) returned %v, want %v;(-want,+got)\n%s",
-				tc.desc, tc.t, got, tc.want, diff)
+			t.Errorf("%s; ListLeaseExpired(%v) returned %v, want %v;(-want,+got)\n%s",
+				tc.desc, tc.cutoff, got, tc.want, diff)
 		}
 	}
 }