diff --git a/Lib/random.py b/Lib/random.py
index 875beb2f8cf41c..768b100786343c 100644
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -246,7 +246,7 @@ def _randbelow_with_getrandbits(self, n):
         "Return a random int in the range [0,n).  Defined for n > 0."
 
         getrandbits = self.getrandbits
-        k = n.bit_length()
+        k = (n - 1).bit_length()
         r = getrandbits(k)  # 0 <= r < 2**k
         while r >= n:
             r = getrandbits(k)
diff --git a/Lib/test/test_generators.py b/Lib/test/test_generators.py
index d48f0d47ba1962..1a4d2d4393669e 100644
--- a/Lib/test/test_generators.py
+++ b/Lib/test/test_generators.py
@@ -1164,22 +1164,22 @@ def b():
  A->F B->B C->C D->D E->F F->F G->G H->H I->I J->J K->B L->L M->M
 merged D into C
  A->F B->B C->C D->C E->F F->F G->G H->H I->I J->J K->B L->L M->M
-merged M into C
- A->F B->B C->C D->C E->F F->F G->G H->H I->I J->J K->B L->L M->C
-merged J into B
- A->F B->B C->C D->C E->F F->F G->G H->H I->I J->B K->B L->L M->C
+merged M into B
+ A->F B->B C->C D->C E->F F->F G->G H->H I->I J->J K->B L->L M->B
+merged H into G
+ A->F B->B C->C D->C E->F F->F G->G H->G I->I J->J K->B L->L M->B
 merged B into C
- A->F B->C C->C D->C E->F F->F G->G H->H I->I J->C K->C L->L M->C
-merged F into G
- A->G B->C C->C D->C E->G F->G G->G H->H I->I J->C K->C L->L M->C
-merged L into C
- A->G B->C C->C D->C E->G F->G G->G H->H I->I J->C K->C L->C M->C
-merged G into I
- A->I B->C C->C D->C E->I F->I G->I H->H I->I J->C K->C L->C M->C
-merged I into H
- A->H B->C C->C D->C E->H F->H G->H H->H I->H J->C K->C L->C M->C
-merged C into H
- A->H B->H C->H D->H E->H F->H G->H H->H I->H J->H K->H L->H M->H
+ A->F B->C C->C D->C E->F F->F G->G H->G I->I J->J K->C L->L M->C
+merged C into G
+ A->F B->G C->G D->G E->F F->F G->G H->G I->I J->J K->G L->L M->G
+merged G into J
+ A->F B->J C->J D->J E->F F->F G->J H->J I->I J->J K->J L->L M->J
+merged J into F
+ A->F B->F C->F D->F E->F F->F G->F H->F I->I J->F K->F L->L M->F
+merged L into F
+ A->F B->F C->F D->F E->F F->F G->F H->F I->I J->F K->F L->F M->F
+merged I into F
+ A->F B->F C->F D->F E->F F->F G->F H->F I->F J->F K->F L->F M->F
 
 """
 # Emacs turd '
diff --git a/Lib/test/test_random.py b/Lib/test/test_random.py
index b1e4ef4197d130..1ad702102c0115 100644
--- a/Lib/test/test_random.py
+++ b/Lib/test/test_random.py
@@ -800,7 +800,7 @@ def test_randrange_uses_getrandbits(self):
         self.gen.seed(1234567)
         # If randrange uses getrandbits, it should pick getrandbits(100)
         # when called with a 100-bits stop argument.
-        self.assertEqual(self.gen.randrange(2**99),
+        self.assertEqual(self.gen.randrange(2**99 + 1),
                          97904845777343510404718956115)
 
     def test_randbelow_logic(self, _log=log, int=int):