Help concerning album art issues on iTunes?

I download music off of Limewire. Yes I know its bad. So, here’s my problem: I download a song that is part of an album. I tweak it so the name and album are properly formatted and spelled. Then I like to copy/paste a nice album cover so everything is organized. Sometimes though, a song will come with picture already that isn’t even of the album. How, and can I change it to stay at the picture I want?