diff --git a/Lib/test/test_random.py b/Lib/test/test_random.py
index 49a3f7bb00f..7d1a53a5507 100644
--- a/Lib/test/test_random.py
+++ b/Lib/test/test_random.py
@@ -240,10 +240,10 @@ def test_bigrand(self):
 
     def test_bigrand_ranges(self):
         for i in [40,80, 160, 200, 211, 250, 375, 512, 550]:
-            start = self.gen.randrange(2 ** i)
-            stop = self.gen.randrange(2 ** (i-2))
+            start = self.gen.randrange(2 ** (i-2))
+            stop = self.gen.randrange(2 ** i)
             if stop <= start:
-                return
+                continue
             self.assertTrue(start <= self.gen.randrange(start, stop) < stop)
 
     def test_rangelimits(self):
@@ -432,10 +432,10 @@ def test_bigrand(self):
 
     def test_bigrand_ranges(self):
         for i in [40,80, 160, 200, 211, 250, 375, 512, 550]:
-            start = self.gen.randrange(2 ** i)
-            stop = self.gen.randrange(2 ** (i-2))
+            start = self.gen.randrange(2 ** (i-2))
+            stop = self.gen.randrange(2 ** i)
             if stop <= start:
-                return
+                continue
             self.assertTrue(start <= self.gen.randrange(start, stop) < stop)
 
     def test_rangelimits(self):
diff --git a/Misc/ACKS b/Misc/ACKS
index 8c2aa4d8a19..36cbdd747f7 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -449,6 +449,7 @@ Dinu Gherman
 Jonathan Giddy
 Johannes Gijsbers
 Michael Gilfix
+Julian Gindi
 Yannick Gingras
 Matt Giuca
 Wim Glenn
diff --git a/Misc/NEWS b/Misc/NEWS
index a3f33099cc5..28382f1c70c 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -21,6 +21,12 @@ Library
 - Issue #19545: Avoid chained exceptions while passing stray % to
   time.strptime().  Initial patch by Claudiu Popa.
 
+Tests
+-----
+
+- Issue #19588: Fixed tests in test_random that were silently skipped most
+  of the time.  Patch by Julian Gindi.
+
 
 What's New in Python 3.4.0 Beta 1?
 ==================================