diff --git a/Lib/test/cmath_testcases.txt b/Lib/test/cmath_testcases.txt
index ce03232..9b08653 100644
--- a/Lib/test/cmath_testcases.txt
+++ b/Lib/test/cmath_testcases.txt
@@ -733,10 +733,11 @@
 ---------------------------
 
 -- zeros
-atan0000 atan 0.0 0.0 -> 0.0 0.0
-atan0001 atan 0.0 -0.0 -> 0.0 -0.0
-atan0002 atan -0.0 0.0 -> -0.0 0.0
-atan0003 atan -0.0 -0.0 -> -0.0 -0.0
+-- These are tested in testAtanSign in test_cmath.py
+-- atan0000 atan 0.0 0.0 -> 0.0 0.0
+-- atan0001 atan 0.0 -0.0 -> 0.0 -0.0
+-- atan0002 atan -0.0 0.0 -> -0.0 0.0
+-- atan0003 atan -0.0 -0.0 -> -0.0 -0.0
 
 -- values along both sides of imaginary axis
 atan0010 atan 0.0 -9.8813129168249309e-324 -> 0.0 -9.8813129168249309e-324
@@ -896,10 +897,11 @@
 ---------------------------------------
 
 -- zeros
-atanh0000 atanh 0.0 0.0 -> 0.0 0.0
-atanh0001 atanh 0.0 -0.0 -> 0.0 -0.0
-atanh0002 atanh -0.0 0.0 -> -0.0 0.0
-atanh0003 atanh -0.0 -0.0 -> -0.0 -0.0
+-- These are tested in testAtanhSign in test_cmath.py
+-- atanh0000 atanh 0.0 0.0 -> 0.0 0.0
+-- atanh0001 atanh 0.0 -0.0 -> 0.0 -0.0
+-- atanh0002 atanh -0.0 0.0 -> -0.0 0.0
+-- atanh0003 atanh -0.0 -0.0 -> -0.0 -0.0
 
 -- values along both sides of real axis
 atanh0010 atanh -9.8813129168249309e-324 0.0 -> -9.8813129168249309e-324 0.0
diff --git a/Lib/test/test_cmath.py b/Lib/test/test_cmath.py
index 0d12635..168b513 100644
--- a/Lib/test/test_cmath.py
+++ b/Lib/test/test_cmath.py
@@ -514,6 +514,24 @@
         for z in complex_zeros:
             self.assertComplexIdentical(cmath.tanh(z), z)
 
+    # The algorithm used for atan and atanh makes use of the system
+    # log1p function; If that system function doesn't respect the sign
+    # of zero, then atan and atanh will also have difficulties with
+    # the sign of complex zeros.
+    @requires_IEEE_754
+    @unittest.skipIf(sysconfig.get_config_var('LOG1P_DROPS_ZERO_SIGN'),
+                     "system log1p() function doesn't preserve the sign")
+    def testAtanSign(self):
+        for z in complex_zeros:
+            self.assertComplexIdentical(cmath.atan(z), z)
+
+    @requires_IEEE_754
+    @unittest.skipIf(sysconfig.get_config_var('LOG1P_DROPS_ZERO_SIGN'),
+                     "system log1p() function doesn't preserve the sign")
+    def testAtanhSign(self):
+        for z in complex_zeros:
+            self.assertComplexIdentical(cmath.atanh(z), z)
+
 
 def test_main():
     run_unittest(CMathTests)