Can you actually open yours Joomla! web site with and without the www.???

Example:
http://yoursitename.com
can also open with;
http://www.yoursitename.com

If you can actually have these show up in your browser then you have a problem.
The problem is Google point of view think they were TWO site and each was getting ranked individually. Not to even mention the perils of duplicate content!
Luckily there is an easy fix. You just need to edit your .htaccess file with the following:

RewriteEngine On
RewriteCond %{HTTP_HOST} ^yoursitename\.com$ [NC]
RewriteRule ^(.*)$ http://www.yoursitename.com/$1 [R=301,L]

Note, in the Joomla htaccess file the "RewriteEngine On" statement is already there, you don't need it twice.

Forget redirects. Do the following;

1. Tell in the Google webmasters page, that http://yoursitename.com and  http://www.yoursitename.com are the same site. Then tell it which you prefer, and it will index your site the way you prefer from then on. The page ranking will be the same.

2. In Joomla, edit the configuration.php file and set "Livesite" to the exact URL you want - with or without "www". Joomla internal links will then display the way you want. You can see what your Livesite variable is set to in "Global Configuration" in the administrator backend, but you must either set it properly when you install Joomla, or manually edit the config file after install. It's not hard.

3. While you're mucking around with your configuration.php file, why not increase your security by moving it out of the public_html directory -