diff --git a/boxtree/tools.py b/boxtree/tools.py
index 5dc58319420b02fee0d39927bc089de51fc44f7a..9c74d960aac4e3c696a9d2e8ade6d3ed8aa13e3f 100644
--- a/boxtree/tools.py
+++ b/boxtree/tools.py
@@ -46,9 +46,9 @@ VectorArg = partial(_VectorArg, with_offset=True)
 AXIS_NAMES = ("x", "y", "z", "w")
 
 
-def padded_bin(i, l):
-    """Format *i* as binary number, pad it to length *l*."""
-    return bin(i)[2:].rjust(l, "0")
+def padded_bin(i, nbits):
+    """Format *i* as binary number, pad it to length *nbits*."""
+    return bin(i)[2:].rjust(nbits, "0")
 
 
 # NOTE: Order of positional args should match GappyCopyAndMapKernel.__call__()
@@ -270,7 +270,7 @@ class DeviceDataRecord(Record):
     instances on the host.
     """
 
-    def _transform_arrays(self, f):
+    def _transform_arrays(self, f, exclude_fields=frozenset()):
         result = {}
 
         def transform_val(val):
@@ -290,6 +290,9 @@ class DeviceDataRecord(Record):
                 return f(val)
 
         for field_name in self.__class__.fields:
+            if field_name in exclude_fields:
+                continue
+
             try:
                 attr = getattr(self, field_name)
             except AttributeError:
@@ -335,9 +338,12 @@ class DeviceDataRecord(Record):
 
         return self._transform_arrays(try_with_queue)
 
-    def to_device(self, queue):
+    def to_device(self, queue, exclude_fields=frozenset()):
         """ Return a copy of `self` in all :class:`numpy.ndarray` arrays are
         transferred to device memory as :class:`pyopencl.array.Array` objects.
+
+        :arg exclude_fields: a :class:`frozenset` containing fields excluding from
+            transferring to the device memory.
         """
 
         def _to_device(attr):
@@ -346,7 +352,7 @@ class DeviceDataRecord(Record):
             else:
                 return attr
 
-        return self._transform_arrays(_to_device)
+        return self._transform_arrays(_to_device, exclude_fields)
 
 # }}}
 
diff --git a/boxtree/tree.py b/boxtree/tree.py
index c09ee65a24960b1eccb993b717e0c3291f5dcf8e..a67a7c2db637610ed08ae04894e8adaeca05d717 100644
--- a/boxtree/tree.py
+++ b/boxtree/tree.py
@@ -389,6 +389,13 @@ class Tree(DeviceDataRecord):
 
     # }}}
 
+    def to_device(self, queue, exclude_fields=frozenset()):
+        # level_start_box_nrs should remain in host memory
+        exclude_fields = set(exclude_fields)
+        exclude_fields.add("level_start_box_nrs")
+
+        return super(Tree, self).to_device(queue, frozenset(exclude_fields))
+
 # }}}
 
 
diff --git a/boxtree/tree_build.py b/boxtree/tree_build.py
index ff944c6ae783e377eeb1771772ea80beec239165..8f652aa8397787b35199e74d18bb2ef041697eb9 100644
--- a/boxtree/tree_build.py
+++ b/boxtree/tree_build.py
@@ -718,8 +718,8 @@ class TreeBuilder(object):
                 # Currently undocumented.
                 lr_lookbehind_levels = kwargs.get("lr_lookbehind", 1)
                 minimal_new_level_length += sum(
-                    2**(l*dimensions) * new_level_leaf_counts[level - l]
-                    for l in range(1, 1 + min(level, lr_lookbehind_levels)))
+                    2**(lev*dimensions) * new_level_leaf_counts[level - lev]
+                    for lev in range(1, 1 + min(level, lr_lookbehind_levels)))
 
             nboxes_minimal = \
                     sum(minimal_upper_level_lengths) + minimal_new_level_length
@@ -740,8 +740,8 @@ class TreeBuilder(object):
                 # Recompute the level padding.
                 for ulevel in range(level):
                     upper_level_padding[ulevel] = sum(
-                        2**(l*dimensions) * new_level_leaf_counts[ulevel - l]
-                        for l in range(
+                        2**(lev*dimensions) * new_level_leaf_counts[ulevel - lev]
+                        for lev in range(
                             1, 1 + min(ulevel, lr_lookbehind_levels)))
 
                 new_upper_level_unused_box_counts = np.max(