I'd recommend running dual systems for about two weeks and slowly moving
traffic over to the new IPs until only your Mail, FTP, WWW, Primary and
Secondary DNS servers are the only machines on the old subnets. Then just
kill the old subnet and move on without a hitch.
Please note that if you have colocates, they will need to make sure that
they update their records with internic also.
For more information about this list (including removal) go to: