diff --git a/sumpy/codegen.py b/sumpy/codegen.py
index b5d1c4ef83d3a4a156334b6007245efa1feb96a0..9c8a4958713800d37c18babd57f2426340a36222 100644
--- a/sumpy/codegen.py
+++ b/sumpy/codegen.py
@@ -80,6 +80,7 @@ class SympyToPymbolicMapper(SympyToPymbolicMapperBase):
 
 # }}}
 
+
 # {{{ bessel handling
 
 BESSEL_PREAMBLE = """//CL//
@@ -215,6 +216,7 @@ def bessel_mangler(kernel, identifier, arg_dtypes):
 class BesselGetter(object):
     def __init__(self, bessel_j_arg_to_top_order):
         self.bessel_j_arg_to_top_order = bessel_j_arg_to_top_order
+        self.cse_cache = {}
 
     @memoize_method
     def hank1_01(self, arg):
@@ -224,26 +226,30 @@ class BesselGetter(object):
     def bessel_jv_two(self, order, arg):
         return prim.Variable("bessel_jv_two")(order, arg)
 
+    def wrap_in_cse(self, expr, prefix):
+        cse = prim.wrap_in_cse(expr, prefix)
+        return self.cse_cache.setdefault(expr, cse)
+
     @memoize_method
     def hankel_1(self, order, arg):
         if order == 0:
-            return prim.Lookup(
-                    prim.CommonSubexpression(self.hank1_01(arg), "hank1_01_result"),
-                    "order0")
+            return self.wrap_in_cse(
+                    prim.Lookup(self.hank1_01(arg), "order0"),
+                    "hank1_01_result")
         elif order == 1:
-            return prim.Lookup(
-                    prim.CommonSubexpression(self.hank1_01(arg), "hank1_01_result"),
-                    "order1")
+            return self.wrap_in_cse(
+                    prim.Lookup(self.hank1_01(arg), "order1"),
+                    "hank1_01_result")
         elif order < 0:
             # AS (9.1.6)
             nu = -order
-            return prim.wrap_in_cse(
-                    (-1)**nu * self.hankel_1(nu, arg),
+            return self.wrap_in_cse(
+                    (-1) ** nu * self.hankel_1(nu, arg),
                     "hank1_neg%d" % nu)
         elif order > 1:
             # AS (9.1.27)
             nu = order-1
-            return prim.CommonSubexpression(
+            return self.wrap_in_cse(
                     2*nu/arg*self.hankel_1(nu, arg)
                     - self.hankel_1(nu-1, arg),
                     "hank1_%d" % order)
@@ -254,22 +260,24 @@ class BesselGetter(object):
     def bessel_j(self, order, arg):
         top_order = self.bessel_j_arg_to_top_order[arg]
 
-        bessel_two = (
-                prim.CommonSubexpression(self.bessel_jv_two(top_order-1, arg),
-                    "bessel_jv_two_result"))
-
         if order == top_order:
-            return prim.Lookup(bessel_two, "jvp1")
+            return self.wrap_in_cse(
+                    prim.Lookup(self.bessel_jv_two(top_order-1, arg), "jvp1"),
+                    "bessel_jv_two_result")
         elif order == top_order-1:
-            return prim.Lookup(bessel_two, "jv")
+            return self.wrap_in_cse(
+                    prim.Lookup(self.bessel_jv_two(top_order-1, arg), "jv"),
+                    "bessel_jv_two_result")
         elif order < 0:
-            return (-1)**order*self.bessel_j(-order, arg)
+            return self.wrap_in_cse(
+                    (-1)**order*self.bessel_j(-order, arg),
+                    "bessel_j_neg%d" % -order)
         else:
             assert abs(order) < top_order
 
             # AS (9.1.27)
             nu = order+1
-            return prim.CommonSubexpression(
+            return self.wrap_in_cse(
                     2*nu/arg*self.bessel_j(nu, arg)
                     - self.bessel_j(nu+1, arg),
                     "bessel_j_%d" % order)