diff --git a/flower/include/pqueue.hh b/flower/include/pqueue.hh
index 981a37e..4c7c259 100644
--- a/flower/include/pqueue.hh
+++ b/flower/include/pqueue.hh
@@ -107,7 +107,44 @@ public:
     T max_t;
     return max_t;
   }
-  void delmin ()
+  void del (vsize i) 
+  {
+    assert (i < size ());
+    T last = heap_array_.back ();
+    heap_array_.pop_back ();
+
+    if (i == size ())
+      return;
+     
+    vsize tgt = ++i;
+
+    vsize next = i / 2;
+    while (next && compare (elt (next), last) > 0) 
+      {
+        elt (tgt) = elt (next);
+        tgt = next;
+        next = tgt / 2;
+      }
+
+    if (tgt == i) 
+      {
+        next = tgt * 2;
+        while (next <= size ()) 
+          {
+            if (((next + 1) <= size ()) &&
+                (compare (elt (next + 1), elt (next)) < 0))
+              next++;
+            if (compare (last, elt (next)) < 0)
+              break;
+            elt (tgt) = elt (next);
+            tgt = next;
+            next = tgt * 2;
+          }
+      }
+    elt (tgt) = last;
+    OK ();
+  }
+  void delmin () 
   {
     assert (size ());
     T last = heap_array_.back ();
diff --git a/lily/include/midi-walker.hh b/lily/include/midi-walker.hh
index 4fd1ae3..3f6c410 100644
--- a/lily/include/midi-walker.hh
+++ b/lily/include/midi-walker.hh
@@ -25,7 +25,7 @@
 #include "lily-proto.hh"
 #include "moment.hh"
 
-struct Midi_note_event : PQueue_ent<int, Midi_note *>
+struct Midi_note_event : PQueue_ent<int, std::pair<int, Midi_note *> >
 {
   bool ignore_;
   Midi_note_event ();
diff --git a/lily/lily-guile.cc b/lily/lily-guile.cc
index 1763a5c..6b5a018 100644
--- a/lily/midi-walker.cc
+++ b/lily/midi-walker.cc
@@ -81,47 +81,56 @@ Midi_walker::do_start_note (Midi_note *note)
 {
   Audio_item *ptr = items_[index_];
   assert (note->audio_ == ptr);
-  int stop_ticks = int (moment_to_real (note->audio_->length_mom_) * Real (384 * 4))
-    + ptr->audio_column_->ticks ();
+  int now_ticks = ptr->audio_column_->ticks ();
+  int stop_ticks = int (moment_to_real (note->audio_->length_mom_) * 
+                        Real (384 * 4)) + now_ticks;
 
-  bool play_start = true;
   for (vsize i = 0; i < stop_note_queue.size (); i++)
     {
-      /* if this pith already in queue */
-      if (stop_note_queue[i].val->get_semitone_pitch ()
+      /* if this pitch already in queue */
+      if (stop_note_queue[i].val.second->get_semitone_pitch ()
 	  == note->get_semitone_pitch ())
 	{
-	  if (stop_note_queue[i].key < stop_ticks)
-	    {
-	      /* let stopnote in queue be ignored,
-		 new stop note wins */
-	      stop_note_queue[i].ignore_ = true;
-
-	      /* don't replay start note, */
-	      play_start = false;
-	      break;
-	    }
-	  else
-	    {
-	      /* skip this stopnote,
-		 don't play the start note */
-	      note = 0;
-	      break;
-	    }
+          if (now_ticks == stop_note_queue[i].val.first)
+            {
+              // The two notes started at the same time.  Merge them.
+              if (stop_note_queue[i].key < stop_ticks)
+                {
+                  Midi_note_event e;
+                  e.val = stop_note_queue[i].val;
+                  e.key = stop_ticks;
+                  stop_note_queue.del (i);
+                  stop_note_queue.insert (e);
+                }
+              note = 0;
+              break;
+            }
+	  else 
+            {
+              // A note was played that interruped a played note.
+              // Stop the old note, and continue to the greatest moment
+              // between the two.
+              if (stop_note_queue[i].key > stop_ticks)
+                {
+                  stop_ticks = stop_note_queue[i].key;
+                }
+              output_event (now_ticks, stop_note_queue[i].val.second);
+              stop_note_queue.del(i);
+              break;
+            }
 	}
     }
 
   if (note)
     {
       Midi_note_event e;
-      e.val = new Midi_note_off (note);
+      e.val = std::make_pair(now_ticks, new Midi_note_off (note));
 
-      midi_events_.push_back (e.val);
-      e.key = int (stop_ticks);
+      midi_events_.push_back (e.val.second);
+      e.key = stop_ticks;
       stop_note_queue.insert (e);
 
-      if (play_start)
-	output_event (ptr->audio_column_->ticks (), note);
+      output_event (ptr->audio_column_->ticks (), note);
     }
 }
 
@@ -137,7 +146,7 @@ Midi_walker::do_stop_notes (int max_ticks)
 	}
 
       int stop_ticks = e.key;
-      Midi_note *note = e.val;
+      Midi_note *note = e.val.second;
 
       output_event (stop_ticks, note);
     }