diff --git a/Doc/howto/ipaddress.rst b/Doc/howto/ipaddress.rst
index 4d9ca08..67cf763 100644
--- a/Doc/howto/ipaddress.rst
+++ b/Doc/howto/ipaddress.rst
@@ -277,23 +277,49 @@
    3221225985
 
 
-Exceptions raised by :mod:`ipaddress`
-=====================================
+Getting more detail when instance creation fails
+================================================
 
 When creating address/network/interface objects using the version-agnostic
-factory functions, any errors will be reported as :exc:`ValueError`.
+factory functions, any errors will be reported as :exc:`ValueError` with
+a generic error message that simply says the passed in value was not
+recognised as an object of that type. The lack of a specific error is
+because it's necessary to know whether the value is *supposed* to be IPv4
+or IPv6 in order to provide more detail on why it has been rejected.
 
-For some use cases, it desirable to know whether it is the address or the
-netmask which is incorrect. To support these use cases, the class
-constructors actually raise the :exc:`ValueError` subclasses
-:exc:`ipaddress.AddressValueError` and :exc:`ipaddress.NetmaskValueError`
-to indicate exactly which part of the definition failed to parse correctly.
+To support use cases where it is useful to have access to this additional
+detail, the individual class constructors actually raise the
+:exc:`ValueError` subclasses :exc:`ipaddress.AddressValueError` and
+:exc:`ipaddress.NetmaskValueError` to indicate exactly which part of
+the definition failed to parse correctly.
 
-Both of the module specific exceptions have :exc:`ValueError` as their
+The error messages are significantly more detailed when using the
+class constructors directly. For example::
+
+   >>> ipaddress.ip_address("192.168.0.256")
+   Traceback (most recent call last):
+     ...
+   ValueError: '192.168.0.256' does not appear to be an IPv4 or IPv6 address
+   >>> ipaddress.IPv4Address("192.168.0.256")
+   Traceback (most recent call last):
+     ...
+   ipaddress.AddressValueError: Octet 256 (> 255) not permitted in '192.168.0.256'
+
+   >>> ipaddress.ip_network("192.168.0.1/64")
+   Traceback (most recent call last):
+     ...
+   ValueError: '192.168.0.1/64' does not appear to be an IPv4 or IPv6 network
+   >>> ipaddress.IPv4Network("192.168.0.1/64")
+   Traceback (most recent call last):
+     ...
+   ipaddress.NetmaskValueError: '64' is not a valid netmask
+
+However, both of the module specific exceptions have :exc:`ValueError` as their
 parent class, so if you're not concerned with the particular type of error,
 you can still write code like the following::
 
    try:
-       ipaddress.IPv4Address(address)
+       network = ipaddress.IPv4Network(address)
    except ValueError:
-       print('address/netmask is invalid:', address)
+       print('address/netmask is invalid for IPv4:', address)
+
diff --git a/Lib/ipaddress.py b/Lib/ipaddress.py
index bd79e2a..e788c0a 100644
--- a/Lib/ipaddress.py
+++ b/Lib/ipaddress.py
@@ -1048,7 +1048,7 @@
             raise ValueError("Ambiguous leading zero in %r not permitted" %
                               octet_str)
         if octet_int > 255:
-            raise ValueError("Octet %d > 255 not permitted" % octet_int)
+            raise ValueError("Octet %d (> 255) not permitted" % octet_int)
         return octet_int
 
     def _string_from_ip_int(self, ip_int):
@@ -1591,7 +1591,8 @@
         hextet_int = int(hextet_str, 16)
         if hextet_int > 0xFFFF:
             # This is unreachable due to the string length check above
-            raise ValueError("Part %d > 0xFFFF not permitted" % hextet_int)
+            msg = "Part 0x%X (> 0xFFFF) not permitted"
+            raise ValueError(msg % hextet_int)
         return hextet_int
 
     def _compress_hextets(self, hextets):
diff --git a/Lib/test/test_ipaddress.py b/Lib/test/test_ipaddress.py
index 61ec0d6..2ac37e1 100644
--- a/Lib/test/test_ipaddress.py
+++ b/Lib/test/test_ipaddress.py
@@ -126,8 +126,8 @@
 
     def test_octet_limit(self):
         def assertBadOctet(addr, octet):
-            msg = "Octet %d > 255 not permitted in %r"
-            with self.assertAddressError(msg, octet, addr):
+            msg = "Octet %d (> 255) not permitted in %r" % (octet, addr)
+            with self.assertAddressError(re.escape(msg)):
                 ipaddress.IPv4Address(addr)
 
         assertBadOctet("12345.67899.-54321.-98765", 12345)
@@ -310,7 +310,7 @@
         assertBadAddress("google.com", "Expected 4 octets")
         assertBadAddress("10/8", "Expected 4 octets")
         assertBadAddress("::1.2.3.4", "Only decimal digits")
-        assertBadAddress("1.2.3.256", "256 > 255")
+        assertBadAddress("1.2.3.256", re.escape("256 (> 255)"))
 
     def test_netmask_errors(self):
         def assertBadNetmask(addr, netmask):