diff --git a/Lib/test/test_random.py b/Lib/test/test_random.py
index efac36a63b9..50d4e94ca22 100644
--- a/Lib/test/test_random.py
+++ b/Lib/test/test_random.py
@@ -758,7 +758,7 @@ class MersenneTwister_TestBasicOps(TestBasicOps, unittest.TestCase):
         # Mersenne Twister randbytes() is deterministic
         # and does not depend on the endian and bitness.
         seed = 8675309
-        expected = b'f\xf9\xa836\xd0\xa4\xf4\x82\x9f\x8f\x19\xf0eo\x02'
+        expected = b'3\xa8\xf9f\xf4\xa4\xd06\x19\x8f\x9f\x82\x02oe\xf0'
 
         self.gen.seed(seed)
         self.assertEqual(self.gen.randbytes(16), expected)
@@ -773,19 +773,35 @@ class MersenneTwister_TestBasicOps(TestBasicOps, unittest.TestCase):
         self.assertEqual(b''.join([self.gen.randbytes(4) for _ in range(4)]),
                          expected)
 
-        # Each randbytes(2) or randbytes(3) call consumes 4 bytes of entropy
+        # Each randbytes(1), randbytes(2) or randbytes(3) call consumes
+        # 4 bytes of entropy
         self.gen.seed(seed)
-        expected2 = b''.join(expected[i:i + 2]
+        expected1 = expected[3::4]
+        self.assertEqual(b''.join(self.gen.randbytes(1) for _ in range(4)),
+                         expected1)
+
+        self.gen.seed(seed)
+        expected2 = b''.join(expected[i + 2: i + 4]
                              for i in range(0, len(expected), 4))
         self.assertEqual(b''.join(self.gen.randbytes(2) for _ in range(4)),
                          expected2)
 
         self.gen.seed(seed)
-        expected3 = b''.join(expected[i:i + 3]
+        expected3 = b''.join(expected[i + 1: i + 4]
                              for i in range(0, len(expected), 4))
         self.assertEqual(b''.join(self.gen.randbytes(3) for _ in range(4)),
                          expected3)
 
+    def test_randbytes_getrandbits(self):
+        # There is a simple relation between randbytes() and getrandbits()
+        seed = 2849427419
+        gen2 = random.Random()
+        self.gen.seed(seed)
+        gen2.seed(seed)
+        for n in range(9):
+            self.assertEqual(self.gen.randbytes(n),
+                             gen2.getrandbits(n * 8).to_bytes(n, 'little'))
+
 
 def gamma(z, sqrt2pi=(2.0*pi)**0.5):
     # Reflection to right half of complex plane
diff --git a/Modules/_randommodule.c b/Modules/_randommodule.c
index 64e44e3bc9f..0fc2d07bb50 100644
--- a/Modules/_randommodule.c
+++ b/Modules/_randommodule.c
@@ -534,31 +534,25 @@ _random_Random_randbytes_impl(RandomObject *self, Py_ssize_t n)
         return NULL;
     }
 
-    if (n == 0) {
-        /* Don't consume any entropy */
-        return PyBytes_FromStringAndSize(NULL, 0);
-    }
-
     PyObject *bytes = PyBytes_FromStringAndSize(NULL, n);
     if (bytes == NULL) {
         return NULL;
     }
     uint8_t *ptr = (uint8_t *)PyBytes_AS_STRING(bytes);
 
-    do {
+    for (; n; ptr += 4, n -= 4) {
         uint32_t word = genrand_uint32(self);
-#if PY_LITTLE_ENDIAN
-        /* Convert to big endian */
+#if PY_BIG_ENDIAN
+        /* Convert to little endian */
         word = _Py_bswap32(word);
 #endif
         if (n < 4) {
-            memcpy(ptr, &word, n);
+            /* Drop least significant bits */
+            memcpy(ptr, (uint8_t *)&word + (4 - n), n);
             break;
         }
         memcpy(ptr, &word, 4);
-        ptr += 4;
-        n -= 4;
-    } while (n);
+    }
 
     return bytes;
 }