diff --git a/sumpy/cse.py b/sumpy/cse.py
index 6a0270e7a31872127dbb0655653a128a5cd5b42c..3318fba023eccbc7673fab31db5d31b0cfeb4035 100644
--- a/sumpy/cse.py
+++ b/sumpy/cse.py
@@ -196,16 +196,19 @@ class FuncArgTracker(object):
             (k, v) for k, v in count_map.items()
             if v >= threshold)
 
-    def get_subset_candidates(self, argset, restrict_to_funcset=frozenset()):
+    def get_subset_candidates(self, argset, restrict_to_funcset=None):
         """
         Return a set of functions each of which whose argument list contains
-        `argset.`
+        `argset`, optionally filtered only to contain functions in
+        `restrict_to_funcset`.
         """
         iarg = iter(argset)
 
         indices = set(
-            fi for fi in self.arg_to_funcset[next(iarg)]
-            if fi in restrict_to_funcset)
+            fi for fi in self.arg_to_funcset[next(iarg)])
+
+        if restrict_to_funcset is not None:
+            indices &= restrict_to_funcset
 
         for arg in iarg:
             indices &= self.arg_to_funcset[arg]