You mean the strings get higher as they get closer to the bridge, right? In that case fiddling with the truss rod isn't gonna help much at all. The truss rod is for adjusting the neck relief, which is the arch or bow of the neck.

To get your strings closer to the high frets you'd wanna look at lowering the action at the bridge as your first port of call. It's possible that you'll have to play around with something else as well to get the action perfect, if lowering the strings at the bridge make's 'em buzz at the low frets. It might possibly involve raising the nut or shimming the neck--both of which are a pain. They're rarely necessary though.