diff --git a/Lib/ipaddress.py b/Lib/ipaddress.py
index 6978483544e621..e805cd0e2a0124 100644
--- a/Lib/ipaddress.py
+++ b/Lib/ipaddress.py
@@ -1150,15 +1150,15 @@ def next_network(self, next_prefix=None):
             ((new_netmask._ip & self.network_address._ip) >> bit_shift) + 1
         ) << bit_shift
 
-        try:
-            return self.__class__(
-                f"{self._string_from_ip_int(next_ip)}/{next_prefix}"
-            )
-        except OverflowError:
+        if next_ip > self._ALL_ONES:
             raise ValueError(
                 f"out of address space, cannot make another /{next_prefix} "
                 "network"
-            ) from None
+            )
+
+        return self.__class__(
+            f"{self._string_from_ip_int(next_ip)}/{next_prefix}"
+        )
 
 
 class _BaseConstants:
diff --git a/Lib/test/test_ipaddress.py b/Lib/test/test_ipaddress.py
index 375d45172a9f4d..d6d0d8220449bd 100644
--- a/Lib/test/test_ipaddress.py
+++ b/Lib/test/test_ipaddress.py
@@ -1596,9 +1596,15 @@ def testNextNetworkWithBadPrefix(self):
 
     def testNextNetworkOutOfAddressSpace(self):
         ipv4 = ipaddress.IPv4Network('255.255.255.0/24')
-        self.assertRaises(ValueError, ipv4.next_network)
+        self.assertRaisesRegex(
+            ValueError,
+            'out of address space, cannot make another /24 network',
+            ipv4.next_network)
         ipv6 = ipaddress.IPv6Network('ffff:ffff:ffff:ffff:ffff:ffff:ffff:0/112')
-        self.assertRaises(ValueError, ipv6.next_network)
+        self.assertRaisesRegex(
+            ValueError,
+            'out of address space, cannot make another /112 network',
+            ipv6.next_network)
 
     def testFancySubnetting(self):
         self.assertEqual(sorted(self.ipv4_network.subnets(prefixlen_diff=3)),