Our solution is to use high-sided plastic tubs for litterboxes - the Sterilite brand, in the 18-gallon size. They're very inexpensive, and they're a good size for most average to large sized cats.
We take the lid off, put about 3 to 4 inches of litter in it, and set a small box next to it so the cats can jump in & out without too much trouble. This completely stops litter being tossed out of the box by overzealous diggers, as well as spray dribbled by the cats who spray up the side of the box, and it prevents 'misses' that can happen if you're lucky enough to have a cat who stands in the box but sticks its behind out of the box to go. With the lid off of the box, they still have the open feeling of an uncovered box, with even better mess confinement than a covered box, because there's no low opening to toss the litter out.
Stepping on the box removes most of the litter from their paws, but we also use a small woven rug on the spot where they jump down from the box (Astroturf-style and ridged mats hurt some cats' paws) to catch additional tracked litter. We keep a little whisk broom & dustpan set by the box to pick up any leftover litter that may drop from their paws in the area. A dustbuster might do the job if you have carpet, or you could use one of these: http://www.petsmart.com/product/inde...ductId=2755050
by the box. They're nice & soft & catch litter well.
If your cat isn't very large, you might consider a Clevercat litter box - it's a bin with a hole in the lid for cats to jump through.