diff --git a/package/MDAnalysis/analysis/density.py b/package/MDAnalysis/analysis/density.py
index 3846d69c17a..c849ba3ea8d 100644
--- a/package/MDAnalysis/analysis/density.py
+++ b/package/MDAnalysis/analysis/density.py
@@ -441,8 +441,11 @@ def _single_frame(self):
         h, _ = np.histogramdd(self._atomgroup.positions,
                               bins=self._bins, range=self._arange,
                               normed=False)
-        # manually reduce (not yet part of AnalysisBase but exists in pmda.parallel.AnalysisBase)
-        self._reduce(self._grid, h)
+        # reduce (proposed change #2542 to match the parallel version in pmda.density)
+        # return self._reduce(self._grid, h)
+        #
+        # serial code can simply do
+        self._grid += h
 
     def _conclude(self):
         # average:
@@ -453,19 +456,21 @@ def _conclude(self):
         density.make_density()
         self.density = density
 
-    @staticmethod
-    def _reduce(res, result_single_frame):
-        """'accumulate' action for a time series
-
-        If `res` is a numpy array, the `result_single_frame` is added to it
-        element-wise. If `res` and `result_single_frame` are lists then
-        `result_single_frame` is appended to `res`.
-        """
-        if isinstance(res, list) and len(res) == 0:
-            res = result_single_frame
-        else:
-            res += result_single_frame
-        return res
+    # _reduce is not strictly necessary for the serial version but is necessary for
+    # pmda-style parallelism (see #2542)
+    # @staticmethod
+    # def _reduce(res, result_single_frame):
+    #     """'accumulate' action for a time series
+    #
+    #     If `res` is a numpy array, the `result_single_frame` is added to it
+    #     element-wise. If `res` and `result_single_frame` are lists then
+    #     `result_single_frame` is appended to `res`.
+    #     """
+    #     if isinstance(res, list) and len(res) == 0:
+    #         res = result_single_frame
+    #     else:
+    #         res += result_single_frame
+    #     return res
 
 
 class Density(Grid):