idling issues

just bought me first mustang. its a 2001 ford mustang gt. whenever i give it gas and then stop abruptly the rpms will dip below normal idle and the car will shake and shudder for a couple seconds before going back up to the normal idle. ive replaced the idle control valve and it did nothing. i dont know if its going to get so bad my car will just die. whats going on?
 
Just a guess because I just did mine. I followed the idle adjustment guide on Stangnet. Mine was running a little rough at the finish of acceleration. Probably was 500 rpm at idle.I bumped it up to 750-800 and its much better in all aspects of low rpm driving. I have a five speed so lots of ups and downs. You have to set it a certain way thats explained here on the idle adjust post. Worth a try. I would also put in a can of Gumout.
 
Go through the tech threads, may be an explanation here