diff --git a/Doc/whatsnew/3.16.rst b/Doc/whatsnew/3.16.rst
index 858dc3b8a878e79..127ba17bab5d2a0 100644
--- a/Doc/whatsnew/3.16.rst
+++ b/Doc/whatsnew/3.16.rst
@@ -412,9 +412,9 @@ io
 ipaddress
 ---------
 
-* Add :meth:`~ipaddress.IPv4Network.next_network` and
-  :meth:`~ipaddress.IPv6Network.next_network` methods to find the next nearest
-  network with a specific prefix size.
+* Add :meth:`IPv4Network.next_network() <ipaddress.IPv4Network.next_network>`
+  and :meth:`IPv6Network.next_network() <ipaddress.IPv6Network.next_network>`
+  methods to find the next nearest network with a specific prefix size.
   (Contributed by Faisal Mahmood in :gh:`87027`.)
 
 
diff --git a/Lib/ipaddress.py b/Lib/ipaddress.py
index 6978483544e621a..de489c0ed034bb0 100644
--- a/Lib/ipaddress.py
+++ b/Lib/ipaddress.py
@@ -1124,11 +1124,15 @@ def next_network(self, next_prefix=None):
 
         Args:
             next_prefix: The desired next prefix length, if not specified the
-            same self.prefixlen will be used
+            same self.prefixlen will be used.
 
         Returns:
             An IPv(4|6) Network object of the next closest network.
 
+        Raises:
+            ValueError: If next_prefix is outside the range of valid prefix
+            lengths, or if no further network of that size exists.
+
         """
         if next_prefix is None:
             next_prefix = self.prefixlen
@@ -1150,15 +1154,13 @@ 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__((next_ip, next_prefix))
 
 
 class _BaseConstants:
diff --git a/Lib/test/test_ipaddress.py b/Lib/test/test_ipaddress.py
index 375d45172a9f4d1..d6d0d8220449bdb 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)),
diff --git a/Misc/NEWS.d/next/Library/2021-01-09-18-40-15.bpo-42861.T7Ge9O.rst b/Misc/NEWS.d/next/Library/2021-01-09-18-40-15.bpo-42861.T7Ge9O.rst
index 46ed99d1e1b4992..9de1e937278152e 100644
--- a/Misc/NEWS.d/next/Library/2021-01-09-18-40-15.bpo-42861.T7Ge9O.rst
+++ b/Misc/NEWS.d/next/Library/2021-01-09-18-40-15.bpo-42861.T7Ge9O.rst
@@ -1,2 +1,3 @@
-Add :meth:`~ipaddress.IPv4Network.next_network` and
-:meth:`~ipaddress.IPv6Network.next_network`.  Patch by Faisal Mahmood.
+Add :meth:`IPv4Network.next_network() <ipaddress.IPv4Network.next_network>`
+and :meth:`IPv6Network.next_network() <ipaddress.IPv6Network.next_network>`.
+Patch by Faisal Mahmood.