Squeaky strings

Thanks to all of the answers I received about my tuning problem. As a newbie, I have one other question. When moving between frets quicklywithout picking up my hand I am getting a lot of annoying sqeaking on the strings. I have used Fast Fret on the strings. That helps the movement, but not the squeaking. I would appreciate any ideas. This is on my McSpadden purchased in November.