Changins on a fender strat?

I just got a beautiful sunburst strat a month ago and decided that it's time to get new strings. When I started to change the strings though, I noticed that every time I would tune the strings from Low E through the High E the Low E would get out of tune until the bridge was all the way up. Once the bridge was all the way up, though, I could use the whammy bar. What can I do to make the bridge stay flat while tuning all the strings?