Ironically enough, I just did new strings on my Precision Monday night. I've changed many, many strings on different basses over the years and have found that generally, removing all is not a problem. There are always gonna be exceptions, but I've had only one, a Ric, that I had to do a good deal of resetting after the change. Removing all is about the only way to clean the board really good, and if your fretboard is rosewood, or I guess anything other than maple, it would be a good time to condition the board with lemon oil or whatever you use. another tip. This an excellent time to condition the strings. Much easier to coat all the way around while it's off. I use Finger-Ease and it works real well for me.
