diff --git a/gtk2_ardour/editor_tempodisplay.cc b/gtk2_ardour/editor_tempodisplay.cc
index 3ccaf78415..3058323c5a 100644
--- a/gtk2_ardour/editor_tempodisplay.cc
+++ b/gtk2_ardour/editor_tempodisplay.cc
@@ -258,7 +258,7 @@ Editor::compute_current_bbt_points (std::vector<TempoMap::BBTPoint>& grid, frame
 
 	/* prevent negative values of leftmost from creeping into tempomap
 	 */
-	const double lower_beat = floor (_session->tempo_map().beat_at_frame (leftmost));
+	const double lower_beat = floor (_session->tempo_map().beat_at_frame (leftmost)) - 1.0;
 	_session->tempo_map().get_grid (grid, max (_session->tempo_map().frame_at_beat (lower_beat), (framepos_t) 0), rightmost);
 }