Do you mean he actually perches along the edge or is he backing up to the edge?
Have you tried looking for storage bins that have a wider ledge, then cut an opening at one end?
I've been looking for a replacement litter box for my cat. The one she's using is my favorite...........3 high sides with one end lower. Might know I can't find it anywhere and am afraid it's no longer made.
The best I've found, and it may work for you, is listed below. Otherwise, I really like the looks of the Smartcat box.

Here is a link that might be useful: litter box

yes, he actually perches on the rim and hangs his butt over the litter, although sometimes he leaves his front paws on the floor, and sometimes he puts his back feet down in the litter. I caught him just now as he was tinkling--he started out with his butt down and then started standing up as he finished. I've seen some pans like the one you showed me, but I"m afraid that he won't like the enclosed feeling and might not use it at all. Did you mean cut a hole in the lid of a storage box? I've not seen one with a very wide rim.

This sort of sounds like what you were looking for--
http://www.amazon.com/Petco-Jumbo-Enclosed-Litter-Box/dp/B003WK0C6C/ref=sr_1_37?s=pet-supplies&ie=UTF8&qid=1375417597&sr=1-37

The link below shows an example of what I was trying to describe. The edges probably aren't wide enough.........and the sides are probably too high for your cat. The search continues........ : )

Here is a link that might be useful: boxes

Ah, I see what you mean--I actually have already used that set up for the other litter pans, although I put a second shallower crate inside the first--I think the gray type are hard to clean because most of them have ridges on the bottoms. Ike will use them, but he usually stands part way out of the doorway and aims backward. This one from petco has possibilities--it sounds like the one you say you used to have.

http://www.petco.com/product/121241/Petco-High-Back-Open-Litter-Pan.aspx?CoreCat=OnSiteSearch

That's it!! I searched their site last night and must have scanned right over it! Thanks for the link.

Must admit that my cat loves to stand outside the lower end of that litter box and continue to cover her business, thus dragging litter out onto the floor. For that reason I place the lower end against a wall. It still allows her easy access but she can no longer play her little game........ : )

glad to be of help. I have a shopping trip planned out of town tomorrow and there's a petco on the way, so I plan to stop and check out their stock. The local petsmart just doesn't have anything that is workable.

You could also try a cement mixing pan (from hardware store). It is really large and gives the cat plenty of room to move around, as well as a sturdy edge. It was a godsend for my old cat with kidney disease as he made so much pee, and it also gave him lots of room to maneuver so he didn't miss the edge or get frustrated. Takes a lot of litter, but if you use scoopable it should work just fine.

Kiddie pools come in all sizes. We have a large one and a smaller one in the garage for when the outdoor cats come inside. They rarely use indoor facilities except when one or more are inside overnight. (They much prefer the wide open spaces of the outdoors which is just fine with me!)

There is a nice edge that seems like it would be 'perchable'.

Thanks for all suggestions. I used to use the cement pans--best litter pans ever for multiple cat households, and also great for 'perchers'. Problem was Ike didn't always 'sit' and the rear of the concrete pans wasn't quite high enough. Also a little large for the area where I need the new pan to go. I found a nice large litter pan at petco (see link above) that I believe will do the trick nicely.