diff --git a/astroplan/scheduling.py b/astroplan/scheduling.py
index 98ca45b7..32f49273 100644
--- a/astroplan/scheduling.py
+++ b/astroplan/scheduling.py
@@ -748,7 +748,7 @@ def _make_schedule(self, blocks):
         score_array = scorer.create_score_array(time_resolution)
 
         # Sort the list of blocks by priority
-        sorted_indices = np.argsort(_block_priorities)
+        sorted_indices = np.argsort(_block_priorities, kind='mergesort')
 
         unscheduled_blocks = []
         # Compute the optimal observation time in priority order
@@ -786,7 +786,7 @@ def _make_schedule(self, blocks):
                 # does not prevent us from fitting it in.
                 # loop over valid times and see if it fits
                 # TODO: speed up by searching multiples of time resolution?
-                for idx in np.argsort(sum_scores)[::-1]:
+                for idx in np.argsort(-sum_scores, kind='mergesort'):
                     if sum_scores[idx] <= 0.0:
                         # we've run through all optimal blocks
                         _is_scheduled = False
diff --git a/astroplan/tests/test_scheduling.py b/astroplan/tests/test_scheduling.py
index 76a35ba7..49d88627 100644
--- a/astroplan/tests/test_scheduling.py
+++ b/astroplan/tests/test_scheduling.py
@@ -158,6 +158,30 @@ def test_priority_scheduler():
     scheduler(blocks, schedule)
     scheduler(blocks, schedule)
 
+    # Check if the order of equal values is respected:
+    # 1. For equal priorities in blocks
+    # 2. For equal scores (boolean_constraint)
+    constraints = [AirmassConstraint(3, boolean_constraint=True)]
+    scheduler.constraints = constraints
+    # Any resolution coarser than this may result in gaps between the blocks
+    scheduler.time_resolution = 20*u.second
+    # This only happens with more than 16 items or so
+    targets_18 = [polaris, polaris, polaris, polaris, polaris, polaris,
+                  polaris, polaris, polaris, polaris, polaris, polaris,
+                  polaris, polaris, polaris, polaris, polaris, polaris]
+    blocks = [ObservingBlock(t, 4*u.minute, 5, name=i) for i, t in enumerate(targets_18)]
+
+    schedule = Schedule(start_time, end_time)
+    scheduler(blocks, schedule)
+
+    for i, t in enumerate(targets_18):
+        # Order of blocks
+        block = schedule.observing_blocks[i]
+        assert block.name == i
+        if i < len(targets_18) - 1:
+            # Same score for all timeslots, should be filled from the start without gaps
+            assert block.end_time.isclose(schedule.observing_blocks[i+1].start_time)
+
 
 def test_sequential_scheduler():
     constraints = [AirmassConstraint(2.5, boolean_constraint=False)]