diff --git a/Lib/test/test_hashlib.py b/Lib/test/test_hashlib.py
index 5b0218b..0f76b24 100644
--- a/Lib/test/test_hashlib.py
+++ b/Lib/test/test_hashlib.py
@@ -560,12 +560,12 @@
 
         constructor(leaf_size=0)
         constructor(leaf_size=(1<<32)-1)
-        self.assertRaises(OverflowError, constructor, leaf_size=-1)
+        self.assertRaises(ValueError, constructor, leaf_size=-1)
         self.assertRaises(OverflowError, constructor, leaf_size=1<<32)
 
         constructor(node_offset=0)
         constructor(node_offset=max_offset)
-        self.assertRaises(OverflowError, constructor, node_offset=-1)
+        self.assertRaises(ValueError, constructor, node_offset=-1)
         self.assertRaises(OverflowError, constructor, node_offset=max_offset+1)
 
         constructor(
diff --git a/Lib/test/test_poll.py b/Lib/test/test_poll.py
index d593495..445032d 100644
--- a/Lib/test/test_poll.py
+++ b/Lib/test/test_poll.py
@@ -159,9 +159,9 @@
             self.fail('Overflow must have occurred')
 
         # Issues #15989, #17919
-        self.assertRaises(OverflowError, pollster.register, 0, -1)
+        self.assertRaises(ValueError, pollster.register, 0, -1)
         self.assertRaises(OverflowError, pollster.register, 0, 1 << 64)
-        self.assertRaises(OverflowError, pollster.modify, 1, -1)
+        self.assertRaises(ValueError, pollster.modify, 1, -1)
         self.assertRaises(OverflowError, pollster.modify, 1, 1 << 64)
 
     @cpython_only