diff --git a/masque/test/test_pack2d.py b/masque/test/test_pack2d.py
index 5390a4c..914c23e 100644
--- a/masque/test/test_pack2d.py
+++ b/masque/test/test_pack2d.py
@@ -1,4 +1,4 @@
-from ..utils.pack2d import maxrects_bssf, pack_patterns
+from ..utils.pack2d import maxrects_bssf, guillotine_bssf_sas, pack_patterns
 from ..library import Library
 from ..pattern import Pattern
 
@@ -25,6 +25,34 @@ def test_maxrects_bssf_reject() -> None:
     assert 0 not in rejects
 
 
+def test_maxrects_bssf_exact_fill_rejects_remaining() -> None:
+    rects = [[20, 20], [1, 1]]
+    containers = [[0, 0, 20, 20]]
+
+    locs, rejects = maxrects_bssf(rects, containers, presort=False, allow_rejects=True)
+
+    assert tuple(locs[0]) == (0.0, 0.0)
+    assert rejects == {1}
+
+
+def test_maxrects_bssf_presort_reject_mapping() -> None:
+    rects = [[10, 12], [19, 14], [13, 11]]
+    containers = [[0, 0, 20, 20]]
+
+    _locs, rejects = maxrects_bssf(rects, containers, presort=True, allow_rejects=True)
+
+    assert rejects == {0, 2}
+
+
+def test_guillotine_bssf_sas_presort_reject_mapping() -> None:
+    rects = [[2, 1], [17, 15], [16, 11]]
+    containers = [[0, 0, 20, 20]]
+
+    _locs, rejects = guillotine_bssf_sas(rects, containers, presort=True, allow_rejects=True)
+
+    assert rejects == {2}
+
+
 def test_pack_patterns() -> None:
     lib = Library()
     p1 = Pattern()
@@ -49,3 +77,20 @@ def test_pack_patterns() -> None:
     # p1 size 10x10, effectively 12x12
     # p2 size 5x5, effectively 7x7
     # Both should fit in 20x20
+
+
+def test_pack_patterns_reject_names_match_original_patterns() -> None:
+    lib = Library()
+    for name, (lx, ly) in {
+            "p0": (10, 12),
+            "p1": (19, 14),
+            "p2": (13, 11),
+            }.items():
+        pat = Pattern()
+        pat.rect((1, 0), xmin=0, xmax=lx, ymin=0, ymax=ly)
+        lib[name] = pat
+
+    pat, rejects = pack_patterns(lib, ["p0", "p1", "p2"], [[0, 0, 20, 20]], spacing=(0, 0))
+
+    assert set(rejects) == {"p0", "p2"}
+    assert set(pat.refs) == {"p1"}
diff --git a/masque/utils/pack2d.py b/masque/utils/pack2d.py
index a99b01e..248f408 100644
--- a/masque/utils/pack2d.py
+++ b/masque/utils/pack2d.py
@@ -60,6 +60,12 @@ def maxrects_bssf(
         degenerate = (min_more & max_less).any(axis=0)
         regions = regions[~degenerate]
 
+        if regions.shape[0] == 0:
+            if allow_rejects:
+                rejected_inds.add(rect_ind)
+                continue
+            raise MasqueError(f'Failed to find a suitable location for rectangle {rect_ind}')
+
         ''' Place the rect '''
         # Best short-side fit (bssf) to pick a region
         region_sizes = regions[:, 2:] - regions[:, :2]
@@ -102,7 +108,7 @@ def maxrects_bssf(
     if presort:
         unsort_order = rect_order.argsort()
         rect_locs = rect_locs[unsort_order]
-        rejected_inds = set(unsort_order[list(rejected_inds)])
+        rejected_inds = {int(rect_order[ii]) for ii in rejected_inds}
 
     return rect_locs, rejected_inds
 
@@ -187,7 +193,7 @@ def guillotine_bssf_sas(
     if presort:
         unsort_order = rect_order.argsort()
         rect_locs = rect_locs[unsort_order]
-        rejected_inds = set(unsort_order[list(rejected_inds)])
+        rejected_inds = {int(rect_order[ii]) for ii in rejected_inds}
 
     return rect_locs, rejected_inds