diff --git a/pint/unit.py b/pint/unit.py
index 27f6b5e..9802822 100644
--- a/pint/unit.py
+++ b/pint/unit.py
@@ -936,18 +936,11 @@ class UnitRegistry(object):
         if check_nonmult and input_units in self._base_units_cache:
             return copy.deepcopy(self._base_units_cache[input_units])
 
-        factor = 1.
-        units = UnitsContainer()
-        for key, value in input_units.items():
-            key = self.get_name(key)
-            reg = self._units[key]
-            if reg.is_base:
-                units.add(key, value)
-            else:
-                fac, uni = self.get_base_units(reg.reference, check_nonmult=False)
-                if factor is not None:
-                    factor *= (reg.converter.scale * fac) ** value
-                units *= uni ** value
+        accumulators = [1., defaultdict(lambda: 0.0)]
+        self._get_base_units(input_units, 1.0, accumulators)
+
+        factor = accumulators[0]
+        units = UnitsContainer(dict((k, v) for k, v in accumulators[1].items() if v != 0.))
 
         # Check if any of the final units is non multiplicative and return None instead.
         if check_nonmult:
@@ -957,6 +950,18 @@ class UnitRegistry(object):
 
         return factor, units
 
+    def _get_base_units(self, ref, exp, accumulators):
+        for key, value in ref.items():
+            key = self.get_name(key)
+            reg = self._units[key]
+            exp2 = exp*value
+            if reg.is_base:
+                accumulators[1][key] += exp2
+            else:
+                accumulators[0] *= reg.converter.scale ** exp2
+                if reg.reference != None:
+                    self._get_base_units(reg.reference, exp2, accumulators)
+
     def get_compatible_units(self, input_units):
         if not input_units:
             return 1., UnitsContainer()