diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index 3fe9071e629d79fe15b283d5097d8022763e948a..e45835d39d64d61f6b75ae18f6444aa4f6ddb44e 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -78,7 +78,7 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             _expansions_in_tree_have_extent=True,
             _expansion_stick_out_factor=0.5,
             _well_sep_is_n_away=2,
-            _max_leaf_refine_weight=32,
+            _max_leaf_refine_weight=None,
             _box_extent_norm=None,
             _from_sep_smaller_crit=None,
             _from_sep_smaller_min_nsources_cumul=None,
@@ -139,6 +139,15 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
                 def fmm_level_to_order(kernel, kernel_args, tree, level):
                     return fmm_order
 
+        if _max_leaf_refine_weight is None:
+            if density_discr.ambient_dim == 2:
+                _max_leaf_refine_weight = 64
+            elif density_discr.ambient_dim == 3:
+                _max_leaf_refine_weight = 128
+            else:
+                # Just guessing...
+                _max_leaf_refine_weight = 64
+
         if _from_sep_smaller_min_nsources_cumul is None:
             # See here for the comment thread that led to these defaults:
             # https://gitlab.tiker.net/inducer/boxtree/merge_requests/28#note_18661
@@ -197,6 +206,7 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             target_association_tolerance=_not_provided,
             _expansions_in_tree_have_extent=_not_provided,
             _expansion_stick_out_factor=_not_provided,
+            _max_leaf_refine_weight=None,
             _tree_kind=None,
             geometry_data_inspector=None,
             fmm_backend=None,
@@ -272,7 +282,8 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
                     if _expansion_stick_out_factor is not _not_provided
                     else self._expansion_stick_out_factor),
                 _well_sep_is_n_away=self._well_sep_is_n_away,
-                _max_leaf_refine_weight=self._max_leaf_refine_weight,
+                _max_leaf_refine_weight=(
+                    _max_leaf_refine_weight or self._max_leaf_refine_weight),
                 _box_extent_norm=self._box_extent_norm,
                 _from_sep_smaller_crit=self._from_sep_smaller_crit,
                 _from_sep_smaller_min_nsources_cumul=(
diff --git a/pytential/qbx/fmm.py b/pytential/qbx/fmm.py
index d3622e5923e2846acd02285303e8e76d7054ad02..4be9e5ca093b5890024f92fb1307ebf42e4fb5f5 100644
--- a/pytential/qbx/fmm.py
+++ b/pytential/qbx/fmm.py
@@ -525,6 +525,7 @@ def drive_fmm(expansion_wrangler, src_weights):
 
 def assemble_performance_data(geo_data, uses_pde_expansions,
         translation_source_power=None, translation_target_power=None,
+        translation_max_power=None,
         summarize_parallel=None, merge_close_lists=True):
     """
     :arg uses_pde_expansions: A :class:`bool` indicating whether the FMM
@@ -573,10 +574,13 @@ def assemble_performance_data(geo_data, uses_pde_expansions,
         if d == 2:
             default_translation_source_power = 1
             default_translation_target_power = 1
+            default_translation_max_power = 0
 
         elif d == 3:
-            default_translation_source_power = 2
-            default_translation_target_power = 1
+            # Based on a reading of FMMlib, i.e. a point-and-shoot FMM.
+            default_translation_source_power = 0
+            default_translation_target_power = 0
+            default_translation_max_power = 3
 
         else:
             raise ValueError("Don't know how to estimate expansion complexities "
@@ -592,11 +596,16 @@ def assemble_performance_data(geo_data, uses_pde_expansions,
         translation_source_power = default_translation_source_power
     if translation_target_power is None:
         translation_target_power = default_translation_target_power
+    if translation_max_power is None:
+        translation_max_power = default_translation_max_power
 
     def xlat_cost(p_source, p_target):
+        from pymbolic.primitives import Max
         return (
                 p_source ** translation_source_power
-                * p_target ** translation_target_power)
+                * p_target ** translation_target_power
+                * Max((p_source, p_target)) ** translation_max_power
+                )
 
     result.update(
             nlevels=tree.nlevels,
@@ -759,11 +768,15 @@ def assemble_performance_data(geo_data, uses_pde_expansions,
     # {{{ form global qbx locals
 
     global_qbx_centers = geo_data.global_qbx_centers()
+
+    # If merge_close_lists is False above, then this builds another traversal
+    # (which is OK).
     qbx_center_to_target_box = geo_data.qbx_center_to_target_box()
     center_to_targets_starts = geo_data.center_to_tree_targets().starts
     qbx_center_to_target_box_source_level = np.empty(
         (tree.nlevels,), dtype=object
     )
+
     for src_level in range(tree.nlevels):
         qbx_center_to_target_box_source_level[src_level] = (
             geo_data.qbx_center_to_target_box_source_level(src_level)