trying to setup the domain mapping for new sites but the new domains keep getting the wordpress subf

My WordPress multisite is setup in a subfolder /wordpress/ and I am trying to setup the domain mapping for new sites but the new domains keep getting the wordpress subfolder name appended to the end of it..

http://www.mydomain.com/wordpress/ -> main site

http://www.clientAdomain.com/wordpress/ -> clients site
which points to: http://www.mydomain.com/wordpress/clientAsite

But need the clients domain name to work without the /wordpress/ subfolder showing:
http://www.clientAdomain.com/

Can I set it up so that the new domains point to the correct site without the WordPress folder name showing after it?

Do I need to change change the location of my wordpress install to not be in a subfolder? I can do this but I imagine this would be a lot of work... Any suggestions on what I can do here? I don't have a lot of clients yet so if I need to change things around now's the time.. Suggestions/recommendations?

Thanks in advance!