diff --git a/storage/merge.go b/storage/merge.go
index 01e667751..f7246c7c8 100644
--- a/storage/merge.go
+++ b/storage/merge.go
@@ -457,6 +457,11 @@ func NewChainSampleIterator(iterators []chunkenc.Iterator) chunkenc.Iterator {
 }
 
 func (c *chainSampleIterator) Seek(t int64) bool {
+	// No-op check
+	if c.curr != nil && c.lastt >= t {
+		return true
+	}
+
 	c.h = samplesIteratorHeap{}
 	for _, iter := range c.iterators {
 		if iter.Seek(t) {
diff --git a/storage/remote/codec.go b/storage/remote/codec.go
index a9f6af0f3..fa033b589 100644
--- a/storage/remote/codec.go
+++ b/storage/remote/codec.go
@@ -357,8 +357,16 @@ func newConcreteSeriersIterator(series *concreteSeries) chunkenc.Iterator {
 
 // Seek implements storage.SeriesIterator.
 func (c *concreteSeriesIterator) Seek(t int64) bool {
-	c.cur = sort.Search(len(c.series.samples), func(n int) bool {
-		return c.series.samples[n].Timestamp >= t
+	if c.cur == -1 {
+		c.cur = 0
+	}
+	// No-op check.
+	if s := c.series.samples[c.cur]; s.Timestamp >= t {
+		return true
+	}
+	// Do binary search between current position and end.
+	c.cur += sort.Search(len(c.series.samples)-c.cur, func(n int) bool {
+		return c.series.samples[n+c.cur].Timestamp >= t
 	})
 	return c.cur < len(c.series.samples)
 }
diff --git a/storage/remote/codec_test.go b/storage/remote/codec_test.go
index b5949cd31..1432736e1 100644
--- a/storage/remote/codec_test.go
+++ b/storage/remote/codec_test.go
@@ -191,6 +191,50 @@ func TestConcreteSeriesClonesLabels(t *testing.T) {
 	require.Equal(t, lbls, gotLabels)
 }
 
+func TestConcreteSeriesIterator(t *testing.T) {
+	series := &concreteSeries{
+		labels: labels.FromStrings("foo", "bar"),
+		samples: []prompb.Sample{
+			{Value: 1, Timestamp: 1},
+			{Value: 1.5, Timestamp: 1},
+			{Value: 2, Timestamp: 2},
+			{Value: 3, Timestamp: 3},
+			{Value: 4, Timestamp: 4},
+		},
+	}
+	it := series.Iterator()
+
+	// Seek to the first sample with ts=1.
+	require.True(t, it.Seek(1))
+	ts, v := it.At()
+	require.Equal(t, int64(1), ts)
+	require.Equal(t, 1., v)
+
+	// Seek one further, next sample still has ts=1.
+	require.True(t, it.Next())
+	ts, v = it.At()
+	require.Equal(t, int64(1), ts)
+	require.Equal(t, 1.5, v)
+
+	// Seek again to 1 and make sure we stay where we are.
+	require.True(t, it.Seek(1))
+	ts, v = it.At()
+	require.Equal(t, int64(1), ts)
+	require.Equal(t, 1.5, v)
+
+	// Another seek.
+	require.True(t, it.Seek(3))
+	ts, v = it.At()
+	require.Equal(t, int64(3), ts)
+	require.Equal(t, 3., v)
+
+	// And we don't go back.
+	require.True(t, it.Seek(2))
+	ts, v = it.At()
+	require.Equal(t, int64(3), ts)
+	require.Equal(t, 3., v)
+}
+
 func TestFromQueryResultWithDuplicates(t *testing.T) {
 	ts1 := prompb.TimeSeries{
 		Labels: []prompb.Label{
diff --git a/storage/series.go b/storage/series.go
index 3a5790c2a..024b0fc72 100644
--- a/storage/series.go
+++ b/storage/series.go
@@ -99,8 +99,12 @@ func (it *listSeriesIterator) Seek(t int64) bool {
 	if it.idx == -1 {
 		it.idx = 0
 	}
+	// No-op check.
+	if s := it.samples.Get(it.idx); s.T() >= t {
+		return true
+	}
 	// Do binary search between current position and end.
-	it.idx = sort.Search(it.samples.Len()-it.idx, func(i int) bool {
+	it.idx += sort.Search(it.samples.Len()-it.idx, func(i int) bool {
 		s := it.samples.Get(i + it.idx)
 		return s.T() >= t
 	})
diff --git a/storage/series_test.go b/storage/series_test.go
new file mode 100644
index 000000000..384009de4
--- /dev/null
+++ b/storage/series_test.go
@@ -0,0 +1,54 @@
+// Copyright 2021 The Prometheus Authors
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package storage
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/require"
+)
+
+func TestListSeriesIterator(t *testing.T) {
+	it := NewListSeriesIterator(samples{sample{0, 0}, sample{1, 1}, sample{1, 1.5}, sample{2, 2}, sample{3, 3}})
+
+	// Seek to the first sample with ts=1.
+	require.True(t, it.Seek(1))
+	ts, v := it.At()
+	require.Equal(t, int64(1), ts)
+	require.Equal(t, 1., v)
+
+	// Seek one further, next sample still has ts=1.
+	require.True(t, it.Next())
+	ts, v = it.At()
+	require.Equal(t, int64(1), ts)
+	require.Equal(t, 1.5, v)
+
+	// Seek again to 1 and make sure we stay where we are.
+	require.True(t, it.Seek(1))
+	ts, v = it.At()
+	require.Equal(t, int64(1), ts)
+	require.Equal(t, 1.5, v)
+
+	// Another seek.
+	require.True(t, it.Seek(3))
+	ts, v = it.At()
+	require.Equal(t, int64(3), ts)
+	require.Equal(t, 3., v)
+
+	// And we don't go back.
+	require.True(t, it.Seek(2))
+	ts, v = it.At()
+	require.Equal(t, int64(3), ts)
+	require.Equal(t, 3., v)
+}
diff --git a/tsdb/tsdbutil/buffer_test.go b/tsdb/tsdbutil/buffer_test.go
index a66786b62..baae8266b 100644
--- a/tsdb/tsdbutil/buffer_test.go
+++ b/tsdb/tsdbutil/buffer_test.go
@@ -159,8 +159,12 @@ func (it *listSeriesIterator) Seek(t int64) bool {
 	if it.idx == -1 {
 		it.idx = 0
 	}
+	// No-op check.
+	if s := it.list[it.idx]; s.T() >= t {
+		return true
+	}
 	// Do binary search between current position and end.
-	it.idx = sort.Search(len(it.list)-it.idx, func(i int) bool {
+	it.idx += sort.Search(len(it.list)-it.idx, func(i int) bool {
 		s := it.list[i+it.idx]
 		return s.t >= t
 	})