diff --git a/libs/temporal/tempo.cc b/libs/temporal/tempo.cc
index e91af44587..5d19053160 100644
--- a/libs/temporal/tempo.cc
+++ b/libs/temporal/tempo.cc
@@ -2774,6 +2774,47 @@ TempoMap::previous_tempo (TempoPoint const & point) const
 	return 0;
 }
 
+TempoPoint const &
+TempoMap::tempo_at (timepos_t const & pos) const
+{
+	if (pos.is_beats()) {
+		return tempo_at (pos.beats());
+	}
+
+	return tempo_at (pos.superclocks());
+}
+
+TempoPoint const &
+TempoMap::tempo_at (superclock_t sc) const
+{
+	assert (!_tempos.empty());
+	Point::sclock_comparator cmp;
+	Tempos::const_iterator t = std::lower_bound (_tempos.begin(), _tempos.end(), sc, cmp);
+	assert (t != _tempos.end());
+	return *t;
+}
+
+
+TempoPoint const &
+TempoMap::tempo_at (Beats const & b) const
+{
+	assert (!_tempos.empty());
+	Point::beat_comparator cmp;
+	Tempos::const_iterator t = std::lower_bound (_tempos.begin(), _tempos.end(), b, cmp);
+	assert (t != _tempos.end());
+	return *t;
+}
+
+TempoPoint const &
+TempoMap::tempo_at (BBT_Time const & bbt) const
+{
+	assert (!_tempos.empty());
+	Point::bbt_comparator cmp;
+	Tempos::const_iterator t = std::lower_bound (_tempos.begin(), _tempos.end(), bbt, cmp);
+	assert (t != _tempos.end());
+	return *t;
+}
+
 TempoMetric
 TempoMap::metric_at (timepos_t const & pos) const
 {
diff --git a/libs/temporal/temporal/tempo.h b/libs/temporal/temporal/tempo.h
index 1707f67e1f..7075807309 100644
--- a/libs/temporal/temporal/tempo.h
+++ b/libs/temporal/temporal/tempo.h
@@ -91,6 +91,9 @@ class /*LIBTEMPORAL_API*/ Point : public point_hook {
 		bool operator() (Point const & a, Point const & b) const {
 			return a.sclock() < b.sclock();
 		}
+		bool operator() (Point const & a, superclock_t sc) const {
+			return a.sclock() < sc;
+		}
 	};
 
 	struct LIBTEMPORAL_API ptr_sclock_comparator {
@@ -103,12 +106,18 @@ class /*LIBTEMPORAL_API*/ Point : public point_hook {
 		bool operator() (Point const & a, Point const & b) const {
 			return a.beats() < b.beats();
 		}
+		bool operator() (Point const & a, Beats const & beats) const {
+			return a.beats() < beats;
+		}
 	};
 
 	struct LIBTEMPORAL_API bbt_comparator {
 		bool operator() (Point const & a, Point const & b) const {
 			return a.bbt() < b.bbt();
 		}
+		bool operator() (Point const & a, BBT_Time const & bbt) const {
+			return a.bbt() < bbt;
+		}
 	};
 
 	/* all time members are supposed to be synced at all times, so we need
@@ -752,10 +761,10 @@ class /*LIBTEMPORAL_API*/ TempoMap : public PBD::StatefulDestructible
 	LIBTEMPORAL_API	MeterPoint const& meter_at (Beats const & b) const { return metric_at (b).meter(); }
 	LIBTEMPORAL_API	MeterPoint const& meter_at (BBT_Time const & bbt) const { return metric_at (bbt).meter(); }
 
-	LIBTEMPORAL_API	TempoPoint const& tempo_at (timepos_t const & p) const { return metric_at (p).tempo(); }
-	LIBTEMPORAL_API	TempoPoint const& tempo_at (superclock_t sc) const { return metric_at (sc).tempo(); }
-	LIBTEMPORAL_API	TempoPoint const& tempo_at (Beats const & b) const { return metric_at (b).tempo(); }
-	LIBTEMPORAL_API TempoPoint const& tempo_at (BBT_Time const & bbt) const { return metric_at (bbt).tempo(); }
+	LIBTEMPORAL_API	TempoPoint const& tempo_at (timepos_t const & p) const;
+	LIBTEMPORAL_API	TempoPoint const& tempo_at (superclock_t sc) const;
+	LIBTEMPORAL_API	TempoPoint const& tempo_at (Beats const & b) const;
+	LIBTEMPORAL_API TempoPoint const& tempo_at (BBT_Time const & bbt) const;
 
 	LIBTEMPORAL_API TempoPoint const* previous_tempo (TempoPoint const &) const;