IMO, most automatic cat litter boxes are more trouble than they are worth. You just want one surface area to clean. No moving parts, nothing to break down. That's why most Quora Answers to “the best litter box” has more to do with a simple box and a good choice of litter.
If you want to significantly reduce the amount of work and the cost of having a litter box for your cat, then use disintegrating pellets with a litter box that sifts the sawdust to a lower level, as described in the Equine Pine Pellets section below.
The following litters are made of pine or corn or wheat. Litter media shouldn't contain toxins or perfumes. Cats have a different sense of smell than humans: any added fragrances should be avoided. A lot of commercial clumping litters are not healthy for cats. They are marketed towards ignorant humans.
Notice there are two strategies covered here. One strategy involves clumping litter, where peeing causes the litter to make a clump. Another strategy is disintegrating litter, where peeing causes large pellets to fall apart and turn to sawdust. With either litter, you can deodorize by sprinkling baking soda on top of the litter.
I list the clumping litter method first, because it is the traditional way, but I prefer the method with the Equine Pine Pellets. That's because I am meticulous about scooping the litter every time I see it's been used.
There are two downsides to the pellets. The poop can be really stinky because the pellets don't cover the poop very well, and because cats may give up trying to cover it since it doesn't work so well. The second downside is that cats prefer a fine grain litter because it's better for digging. It satisfies their instinctive need for digging and covering of their waste.
A third option I'm covering as an afterthought, is the use of non-clumping, non-disintegrating, litter, often made of clay. With clay litter, you change out the whole box more often than with clumping litter. You may not even scoop at all. A skilled cat will keep it tidy. Your attempt at digging out poop can just stir the urinated litter into the clean litter. You can go through a LOT of litter with this method. The smell can be an issue, so this works best in a well ventilated area like a garage or catio (patio). You would use the same type of litter boxes as for clumping litter, but not the sifting ones. There's a good Q&A on Chewy that I got a picture of, just in case it disappears.
Also check out diatomaceous earth litter, covered in the addendum. I'm not sure if it's available everywhere.
Humane Society complements this article by providing background knowledge not covered here.
With clumping litter, peeing causes wet litter to agglomerate so you can scoop it. Scooping should be frequent, because, while the clumps hold together, if allowed to dry for a day or more, you end up with clumps that have shed a lot of corn-pee-dust. One brand I've used that works well is World's Best Cat Litter, which is made from corn and can be flushed in the toilet. I've also heard of litter made of wheat or walnut shells, but I haven't tried them.
The best litter boxes are large and have high walls, such as the NVR miss litterbox, or a large tupperware storage box with an entrance cut into the long side of the box. Cats align themselves with the cat box to do their business, and if you have one that tends to pee high, it will not be toward the entrance.
If you want something that has a roof, IMO it's better to use a small dog house over a conventional cat box, rather than a cat box with a built in roof. I don't really like a roof because I want to be able to see the status of the litter without having to remove anything, especially if it has an exact fit or latches to fuddle with.
The best cat box can be a tall tupperware container, as seen in this video, where a circular entrance is cut out of the long side of the box. It's best if the box is totally clear, so “the cat can see who's coming, and anticipate what might be lurking on the outside when they exit the box.” This closed box is superior to two piece boxes where the top half seal overhangs the bottom half, and urine aimed high on the wall can drip through to the floor.
Update: This top entry litter box has a roof with a mesh that reduces litter scatter. As the cat climbs out their paw will step on the mesh. It's best to place the entry side of the box adjacent to a wall, so the cat must step on the roof rather than jump straight out to the floor.
You can also use some sifting litter boxes, which include two boxes and one sifter that stack together. You sift all the litter through the sieve, leaving the clumps and poop on the sieve surface, and trash that. Then you pick up the top box with the litter, and pour the litter onto the sieve and second box stack. This is a lot of pouring of cat litter, so I would only use this outside, because cat litter, no matter how “dust free” it says it is, has always made a dust cloud for me. Who knows, there is some litter that claims to be 100% dust free, but I haven't tried it.
This is my favorite litter system, because you only have to scoop the poopsies. More benefits are in the sifting litter boxes section below.
Equine pellets are used for horse bedding, usually sold in 40 lb bags, and priced at $5.99 at the Tractor Supply. The same stuff is available from other sources at inflated prices. Pine must be cooked or “kiln dried” at high temperature, to remove the pine oils that are toxic to cats.
“I called Tractor Supply and was referred to the vendor who actually manufactured the bag of pelletized bedding… I was told they actually bake it at a much higher heat degree than a kiln, and twice. Which leaves no allergens or oils in the product. It is then pressed reducing even further the above mentioned.” Quote is from a comment below this video. More info here.
I don't think the wood pellets for fuel are the same thing.
Peeing on the pellets causes them to turn to sawdust, which can be self-sifting to a lower level under the top level where the cat uses the litter. In other words, the litter sits on the top level, which has a mesh that acts as a sieve, allowing the pee-dust to work its way to the lower level. The lower level can be covered with a dog-pee mat. You still scoop out the poop from the top level. Both you and your cat encourage the sifting process by digging through the litter. Kicking / shaking the box is also effective. The depth of the pellets in the box should not be more than two inches. More than 2“ will function, but will make sifting more difficult.
The advantages of this method:
I have only found two litter boxes designed for this purpose, available in the USA. The Breeze Box, and the All Pine Litter Box. Further searching revealed other manufacturers in other countries, detailed in a section below.
I learned about this method in this video. The video is made by the owner of Victorian Gardens Cattery, which includes links to boxes and supplies that work together well. Recommended by the lady is a height of at least 3 inches, preferably 4, between the sifting surface and the bottom surface. This is accomplished by replacing the lower section of the Breeze box with a plain litter box that has the correct dimensions, such that the sifting Breeze box sits elevated on the edges of the box. The video makes this clear.
Alternatively, you can make your own with DIY pine litter box instructions: https://www.instructables.com/id/How-to-build-a-Feline-Pine-self-cleaning-litter-bo
Although, I think slots work better than drill holes. Also, with these instructions, you will need to glue some PVC pipe stilts to the bottom of the sifter so there is a taller gap between the boxes.
Below is a picture of some stilts in action, on a litterbox called the All Pine Litter Box, which doesn't have enough clearance for more than a few days of litter usage by a hoard of cats. It could be fine for one cat. Your mileage may vary.
Also working, according to some comments under the video and in the reviews at amazon, is the Arm and Hammer sifting cat box, as the holes are narrower than the size of the pellets. You do need to modify the box so that the sieve/sifting box is elevated from the lower box. One guy used hot melt glue to attach foam blocks to the sides of the sieve/sifting box.
Update 20200530:
I got an Arm and Hammer sifting litter box, and it works great! In particular, it sifts better than the Breeze Box. There are sieve slots throughout the bottom surface, rather than localized in the center area, which makes sifting more efficient. Cats usually pee near the edges of the box, so on the Breeze Box, you usually find an accumulation of unsifted sawdust, that is harder to sift than if the sieve slots were right underneath.
The Arm & Hammer sieve slots are also wider, and because of this, some small pieces of pellets fall through. But this is beneficial, because some extra sawdust is needed down there to absorb odor. I found that I don't need the baking soda, because the sawdust in the lower level stays dry and there is no ammonia smell.
I modified the Arm & Hammer box using 1” PVC pipe, and duct tape. Technically, 1“ PVC has an outer diameter of 1.315 inches. It was a quick fix and in the future I can improve it. There are many more examples in the customer images on Amazon.
The sifting slots have to be the right width. Too narrow, and the sawdust clogs the slot. With a larger slot, the pellets may be caught and won't move out of the slot when cats dig or you stir the litter. If the slot is too large, the pellets just fall through.
Wondering about the slots in sifting litter boxes, I went to Petsmart, and looked at their sifting litter box selection, which included the Breeze box recommended in the video. The slots of the Breeze box are more narrow compared to slots on boxes made for fine-grain litter, where the litter is intended to fall through. Even if the pellets don't fall through, I think in practice the slots/holes are big enough that the pellets become stuck and cover the holes. While stirring the litter with the scooper, it will be harder for them to move out of the way for the sawdust to fall through. Below are pictures comparing the Breeze slots with the other three boxes:
This one is the Van Ness XL sifting litter box, which has holes so big the pellets just fall through:
One thing to note, is that the newer version of the Breeze box (pictured above) has slightly narrower slots than the previous model. The lady in the video said the older Breeze boxes are better because they sift the pine pellet sawdust better.
It's crazy how there are so many awesome products we never even hear about. Someone at NYCACC told me about a litter box they got in Europe, and I also found British and Australian manufacturers:
https://www.peeweeinternational.eu/index.php
https://brit-pet.com/collections/our-products
https://www.oz-pet.net.au/cat-loo-info
https://www.catmate.com.au/products
They have many models, and they are made for wood pellets! The Breeze box is too tiny for an adult cat, so it's nice to see larger options. As an aside, my favorite bicycle lock was European, and no one in the U.S. had ever heard about it. If European products can be kept secret, I wonder what other phenomena, such as the news, can also be kept secret.
I got a response from Brit-Pet, in the comments section at the bottom of the article, which says they can ship their boxes to USA.
I also got a response from Pee Wee in an email, that says:
Unfortunately we don’t have a distributor in the USA at the moment. Hopefully we will be available in your country soon.
You can maybe contact Pets Gifts, they are a selling point here in the Netherlands and maybe they can help you.
There e-mail address is contact@petsgifts.nl.
Below a size comparison of Exquisicat pine pellets with Breeze box system pellets made of zeolite, as they appear on the bag photos. The next picture down, are actual diameters of Feline Pine (largest), zeolite Breeze pellets, and Feline Fresh Pine Pleets (smallest). You cannot use Feline Fresh with the Arm & Hammer Box, because the pellets fall through the slots in the sieve.
In searching to see if zeolite dust might be toxic, I came across a study. There was no evidence of harm from ingestion. There was no difference in respiratory disease occurrence between the exposed and the control group (the rats were pretty old when examined). MSDS for zeolite doesn't show cause for alarm. So it appears that either pine pellets or zeolite is fine and one can choose what is less expensive. If you are close to a Tractor Supply, that would be the horse bedding pine pellets.
Update: I mixed the pine pellets and the zeolite pelles together in the same litter box, and have found that the zeolite pellets last forever. Do they even dissolve? They stay around forever. How unhygienic. That would explain the much smaller clearance for dust in the Breeze box collection bin, and the extremely thick Breeze branded pee pads. I like the sawdust from pine pellets, as I think its ability to absorb pee helps maintain the cleanliness of the sieve surface.
I moved to another country, and started using diatomaceous earth, as I didn't have too many other options. Luckily, my cat almost always poops outside, so the litter box is rarely used except for peeing when the door to the back yard is closed. The litter sticks to the poop as individual rocks, and keeps from dirtying the sifter. As for the pee, I'm not sure where it goes. The litter seems highly absorbent. There are no wet spots after a month of light use with the original 2 Kg of litter. Because my cat goes outside mostly, I can't directly compare to previous litter box methods. However, I have no complaints with this litter!
Update: I stayed at another location without a yard, and the litter lasted for 3 weeks before it started smelling of ammonia. I filled the box with 4 Kg this time. For clay litter, humane society says: “Twice a week is a general guideline for replacing clay litter, but depending on your circumstances, you may need to replace it every other day or only once a week.” So this diatomaceous earth litter must be much more absorbent than clay.
Inhaled diatomaceous earth can have silica that is harmful to the lungs. However, I don't see much of a dust cloud when pouring the coarse grain litter I'm using (unlike my experience with clay litter).