diff --git a/Lib/test/test_functools.py b/Lib/test/test_functools.py
index e8cf848..632b2d3 100644
--- a/Lib/test/test_functools.py
+++ b/Lib/test/test_functools.py
@@ -1102,43 +1102,76 @@
 
     @unittest.skipUnless(threading, 'This test requires threading.')
     def test_lru_cache_threaded(self):
+        n, m = 5, 11
         def orig(x, y):
             return 3 * x + y
-        f = self.module.lru_cache(maxsize=20)(orig)
+        f = self.module.lru_cache(maxsize=n*m)(orig)
         hits, misses, maxsize, currsize = f.cache_info()
         self.assertEqual(currsize, 0)
 
+        start = threading.Event()
         def full(f, *args):
-            for _ in range(10):
+            start.wait(10)
+            for _ in range(m):
                 f(*args)
 
-        def clear(f):
-            for _ in range(10):
+        def clear():
+            start.wait(10)
+            for _ in range(2*m):
                 f.cache_clear()
 
         orig_si = sys.getswitchinterval()
         sys.setswitchinterval(1e-6)
         try:
-            # create 5 threads in order to fill cache
+            # create n threads in order to fill cache
             threads = [threading.Thread(target=full, args=[f, k, k])
-                       for k in range(5)]
+                       for k in range(n)]
             with support.start_threads(threads):
-                pass
+                start.set()
 
             hits, misses, maxsize, currsize = f.cache_info()
-            self.assertEqual(hits, 45)
-            self.assertEqual(misses, 5)
-            self.assertEqual(currsize, 5)
+            self.assertLessEqual(misses, n)
+            self.assertEqual(hits, m*n - misses)
+            self.assertEqual(currsize, n)
 
-            # create 5 threads in order to fill cache and 1 to clear it
-            threads = [threading.Thread(target=clear, args=[f])]
+            # create n threads in order to fill cache and 1 to clear it
+            threads = [threading.Thread(target=clear)]
             threads += [threading.Thread(target=full, args=[f, k, k])
-                        for k in range(5)]
+                        for k in range(n)]
+            start.clear()
             with support.start_threads(threads):
-                pass
+                start.set()
         finally:
             sys.setswitchinterval(orig_si)
 
+    @unittest.skipUnless(threading, 'This test requires threading.')
+    def test_lru_cache_threaded2(self):
+        # Simultaneous call with the same arguments
+        n, m = 5, 7
+        start = threading.Barrier(n+1)
+        pause = threading.Barrier(n+1)
+        stop = threading.Barrier(n+1)
+        @self.module.lru_cache(maxsize=m*n)
+        def f(x):
+            pause.wait(10)
+            return 3 * x
+        self.assertEqual(f.cache_info(), (0, 0, m*n, 0))
+        def test():
+            for i in range(m):
+                start.wait(10)
+                self.assertEqual(f(i), 3 * i)
+                stop.wait(10)
+        threads = [threading.Thread(target=test) for k in range(n)]
+        with support.start_threads(threads):
+            for i in range(m):
+                start.wait(10)
+                stop.reset()
+                pause.wait(10)
+                start.reset()
+                stop.wait(10)
+                pause.reset()
+                self.assertEqual(f.cache_info(), (0, (i+1)*n, m*n, i+1))
+
     def test_need_for_rlock(self):
         # This will deadlock on an LRU cache that uses a regular lock