diff --git a/storage/remote/codec_test.go b/storage/remote/codec_test.go
index 1432736e1..be52bd312 100644
--- a/storage/remote/codec_test.go
+++ b/storage/remote/codec_test.go
@@ -233,6 +233,11 @@ func TestConcreteSeriesIterator(t *testing.T) {
 	ts, v = it.At()
 	require.Equal(t, int64(3), ts)
 	require.Equal(t, 3., v)
+
+	// Seek beyond the end.
+	require.False(t, it.Seek(5))
+	// And we don't go back. (This exposes issue #10027.)
+	require.False(t, it.Seek(2))
 }
 
 func TestFromQueryResultWithDuplicates(t *testing.T) {
diff --git a/storage/series_test.go b/storage/series_test.go
index 384009de4..8ce4a7222 100644
--- a/storage/series_test.go
+++ b/storage/series_test.go
@@ -51,4 +51,9 @@ func TestListSeriesIterator(t *testing.T) {
 	ts, v = it.At()
 	require.Equal(t, int64(3), ts)
 	require.Equal(t, 3., v)
+
+	// Seek beyond the end.
+	require.False(t, it.Seek(5))
+	// And we don't go back. (This exposes issue #10027.)
+	require.False(t, it.Seek(2))
 }