Search Engines will view www.yoursite.com and yoursite.com as two different entities dividing your SEO performance. One easy fix is to implement a canonical redirect using your .HTACCESS file
Point www.mysite.com to mysite.com
Options +FollowSymLinks
RewriteEngine On
RewriteCond %{HTTP_HOST} !^domain\.com$
RewriteRule (.*) http://domain.com/$1
[R=301,L]
Point oldsite.com to www.newsite.com
Options +FollowSymLinks
RewriteEngine On
RewriteCond %{HTTP_HOST} !^www\.yoursite\.com$
RewriteRule (.*) http://www.yoursite.com/$1 [R=301,L]