My mother in law has a new kitten that is like this, she does not want to go once it's been used. The problem that I saw, when I went to see if I could help figure out why she had pooped outside of the box on a few occasions, she was not putting enough litter in the box. She was trying to just put a very small amount. It was unscented litter, and with it being such a small amount she was using, the smell of the litter box was horrific. I told her to clean the litter box, very well, fill it with at least 4 inches of litter, which is pretty much all of a 20 pound container, and to scoop it twice a day, or more, if you are there when she goes. When you use a really small amount of litter, the litter box just gets gross, really fast, at least I think it does. My mother in law is using the Dr. Elsey's Cat Attract litter right now, and it is unscented, but since she has been keeping it full and scooped, the kitten has not had any incidents going outside the box. I told her to add some baking soda to the litter, mix it in, it really seemed to help too with the strong urine smell. I would try a good clumping litter, like Tidy Cat, and use the whole container. Then, as you scoop out the used part, add more to the box to keep it topped off. I have a very, very picky cat, who will not go into the box if it has poop in it, and even he is fine with it as long as there is enough in there and it is topped off and the poop is scooped out of it. You really won't go through litter as much as the way you are doing it, just putting a small amount in and changing it. If there is a small amount of litter in the box, it is going to smell, really bad, even if you scoop it.