diff --git a/libs/ardour/midi_clock_slave.cc b/libs/ardour/midi_clock_slave.cc
index 4c73c45f49..16f4544062 100644
--- a/libs/ardour/midi_clock_slave.cc
+++ b/libs/ardour/midi_clock_slave.cc
@@ -346,6 +346,10 @@ MIDIClock_Slave::speed_and_position (double& speed, nframes64_t& pos)
 
 	// calculate speed
 	speed = ((t1 - t0) * session->frame_rate()) / one_ppqn_in_frames;
+	
+	// provide a 3% deadzone to lock the speed
+	if (fabs(speed - 1.0) <= 0.03)
+	        speed = 1.0;
 
 	// calculate position
 	if (engine_now > last_timestamp) {
diff --git a/libs/ardour/test/midi_clock_slave_test.cpp b/libs/ardour/test/midi_clock_slave_test.cpp
index 1fc0ef7dc1..a555558c3d 100644
--- a/libs/ardour/test/midi_clock_slave_test.cpp
+++ b/libs/ardour/test/midi_clock_slave_test.cpp
@@ -15,9 +15,10 @@ MIDIClock_SlaveTest::testStepResponse ()
   MIDI::Parser* parser = 0;
 
   TestSlaveSessionProxy *sess = (TestSlaveSessionProxy *) session;
-  nframes64_t period_size = 1024;
+  nframes64_t period_size = 4096;
   sess->set_period_size (period_size);
-  
+
+  bandwidth = 1.0 / 60.0;
 
   nframes64_t start_time = 1000000;
   start (*parser, start_time);