IMO, a SCOTUS justice can use other cases for guidance, but must give the most weight to their reading of the Constitution. So if a case came up that had already been decided (let's say Roe v Wade) by a prior court - and the current court felt a plain reading of the Constitution does not agree with the ruling - the strict constructionist method would be to overturn the previous ruling.
FWIW, I also believe a court should give greater weight to statute than prior rulings, but of course less weight than the Constitution is accorded.
What's ironic about some of the conservative posters on this thread, complaining about a single constructionist ruling by Gonzales, is that the left is absolutely terrified of the concept of strict constructionism. So these few posters are playing into their hands by demanding that Gonzales states his personal views on issues, which will give the libs ammo to shoot at him.
Each branch has spent decades usurping their current level of power, they're not about to throw it out overnight by actually following the Constitution...