The large rug under the litter box is the answer - pick up the rug and shake it out - no vacuuming at all!
I got a new Oreck - the best vacuum I've ever owned; it picks up everything in it's tracks... and is easy to use. I have a mother cat and 4 little ones in the house - so lots to pick up - don't know where they find most of what I have to vacuum - thought i was a fair housekeeper! But, I run the vacuum over the floors and it's gone!