My cat does use the litter box, but her little bottom does not always clear the entrance. Thus she often pees just outside the box. When she poops she does go entirely inside the box as she should. Just when she pees she misses the mark. I use a standard covered box. Any suggestions?

That is a common problem with cats. I would suggest trying a cover but you already have. Maybe a bigger box?

I don't know if this helps at all but you can buy kitty litter boxes that are covered and they have a cat flap at the front...
You could separate the inside of it so the kitty litter is at the back she should go all the way in to the litter before she 'does her business'