diff --git a/boxtree/tree_build.py b/boxtree/tree_build.py
index 2566dc44de18e858fff799457d8960fc8997c9d2..b03c336e53205b5e61e2c91ce7c57610aeb295f3 100644
--- a/boxtree/tree_build.py
+++ b/boxtree/tree_build.py
@@ -36,6 +36,10 @@ import logging
 logger = logging.getLogger(__name__)
 
 
+class MaxLevelsExceeded(RuntimeError):
+    pass
+
+
 class TreeBuilder(object):
     def __init__(self, context):
         """
@@ -454,7 +458,8 @@ class TreeBuilder(object):
                 queue, box_parent_ids.data, np.zeros((), dtype=box_parent_ids.dtype))
         prep_events.append(evt)
 
-        nlevels_max = np.iinfo(self.box_level_dtype).max
+        nlevels_max = np.finfo(coord_dtype).nmant + 1  # num bits in the significand
+        assert nlevels_max <= np.iinfo(self.box_level_dtype).max
 
         # level -> starting box on level
         level_start_box_nrs_dev, evt = zeros(nlevels_max, dtype=box_id_dtype)
@@ -540,8 +545,11 @@ class TreeBuilder(object):
                 assert level == len(level_used_box_counts)
                 assert level == len(level_leaf_counts)
 
-            if level > np.iinfo(self.box_level_dtype).max:
-                raise RuntimeError("level count exceeded maximum")
+            if level + 1 >= nlevels_max:  # level is zero-based
+                raise MaxLevelsExceeded("Level count exceeded number of significant "
+                        "bits in coordinate dtype. That means that a large number "
+                        "of particles was indistinguishable up to floating point "
+                        "precision (because they ended up in the same box).")
 
             common_args = ((morton_bin_counts, morton_nrs,
                     box_start_flags,
diff --git a/test/test_tree.py b/test/test_tree.py
index f68a885edf93ff5828e37ca4d1e4af81c866f91b..cf5e11063ee50c6904a025ece55f0be082c30f39 100644
--- a/test/test_tree.py
+++ b/test/test_tree.py
@@ -1122,6 +1122,25 @@ def test_same_tree_with_zero_weight_particles(ctx_factory, dims):
 # }}}
 
 
+# {{{ test_max_levels_error
+
+def test_max_levels_error(ctx_factory):
+    ctx = ctx_factory()
+    queue = cl.CommandQueue(ctx)
+
+    from boxtree import TreeBuilder
+    tb = TreeBuilder(ctx)
+
+    logging.basicConfig(level=logging.INFO)
+
+    sources = [cl.array.zeros(queue, 11, float) for i in range(2)]
+    from boxtree.tree_build import MaxLevelsExceeded
+    with pytest.raises(MaxLevelsExceeded):
+        tree, _ = tb(queue, sources, max_particles_in_box=10, debug=True)
+
+# }}}
+
+
 # You can test individual routines by typing
 # $ python test_tree.py 'test_routine(cl.create_some_context)'