How to make karaoke sound tracks?

Is there a way to legally strip the lead vocals (and maybe the backup vocals) off of legally downloaded music videos in order to be able to sing them at karaoke? I know that there are thousands of songs already sold that way commercially, but sometimes you run across a song that you would like to sing and cannot find it as a karaoke song. I'm assuming that getting the artist's or publisher's permission would be the first step.