Rollover Menu problem

I have 3 tabs, each in movie clips set up like the drop down tutorial on this site -
when you rollover the tab, it plays an animation that brings in the subnavigation,


…and if you roll over a large button outside that area, it plays a short clip that makes the subnav disappear. The problem I have is this only works if you move the mouse slowly. If you move it at normal speed, it seems to miss the actionscript to get rid of the first subnav on(rollOver){

…and just puts the next subnav over top of it. Is there any way around this other than moving the 3 tabs far away from wach other?