phranque - 1:07 pm on Mar 27, 2013 (gmt 0)
welcome to WebmasterWorld, Jimb0!
i would not do any links from your new site or redirects.
if there is a specifically defined list or identifiable pattern of urls from the previous site that don't conflict with your new urls, you could do as lucy24 suggested and provide a 404 or 410 status code and a custom error document for those requests if possible.
if you are on an apache server you could probably do this all in .htaccess using the [G] flag for the RewriteRule directive and limiting the ErrorDocument directive within a Location or LocationMatch container.