Hello Paul, I'm Dr. Deb and will do my best to help you today.
I'm sorry for this concern your cat. As you might suspect, inappropriate elimination issues are not uncommon in cats and can be quite upsetting.
For some cats, there's a simple solution to this problem but for others, it's a little more complicated.
I'm going to assume that the stools are not loose but a normal consistency; if they aren't, then please let me know.
Cats often use urination and defecation as a means of communication with other cats (if more than one is present in the household) or psychological stress can also trigger inappropriate elimination as well. However, when a cat is using the litter to urinate but not using it to defecated, then in my experience, the reason most frequently will trace back to the litter box and/or litter itself.
Much research has been done on this topic ....litter and box preferences...and the following is a summary of this research as well as other problems which might trigger inappropriate defecation. Some or all of these may not apply, but I want to include them to be complete.
1. Some cats like a very clean box; when it becomes dirtier than they prefer, they'll defecate elsewhere. So, the box should be scooped at least daily or twice daily and the entire box cleaned weekly with soap and water; avoid harsh smelling chemicals.
2. The number of boxes and size is important: The rule of thumb is one box/cat plus one box. A litter box length should be at least one and a half times the length of the cat (not including the tail) so they have adequate space to maneuver and cover excrement.
3. Cats prefer clumping litter.
4. Cats prefer unscented litter.
5. Cats don't like hoods on their boxes because they retain odors.
6. There is something about the texture of the litter that they don't like, for what ever reason. This is known as Litter Aversion and is a fairly common problem. One way to know if this might be the issue is if there is minimal digging or disturbance of the litter that's in the box. Digging is a natural instinct to cover waste material, especially feces. If they don't like the texture of the litter, they don't want to touch it with their feet.
7. They have associated pain with the box when they had a bowel movement in their box and don't want to repeat the experience.
8. Cats don't like their boxes where there's a of noise or foot traffic; they prefer privacy.
9. Use of enzymatic cleaners to degrade the fecal material rather than just cover up the odor (the cats can still detect it) are preferred.
Other helpful hints in addition to the above:
1. Use of Cat Attract in the litter
2. Sometimes confinement in a smaller room/space with food/water and the litter to "retrain" them can be useful.
3. It may not be convenient, but mixing sand or dirt with the litter may make it more appealing.
4. This helpful hint isn't practical for most owners and their cats but if you were able to "catch" him ever using the litter to defecate and he likes tasty treats such as Pounce, then he could be rewarded every time he uses the box...applying basic behavior modification techniques of positve reinforcement. But, as I said, this isn't too practical for most owners, unfortunately. Another instance where cats are not small dogs and can't be treated as such.
There are some vets who believe that inappropriate defection issues may be related to underlying medical issues such as Inflammatory Bowel Disease or polyps or stricture for example, even if the stools are a normal consistency. They'll often suggest that x-rays and a rectal under sedation be done to look for abnormalities.
Some gastroenterologists recommend or suggest a low-residue diet, or a low-carb canned diet (carbs < 7%). This LINK provides this information for a large number of semi-moist and canned foods.
It's clear that for some cats, Inflammatory Bowel Disease issues may be the cause of their inappropriate defecation issues which will resolve with the use of limited ingredient diets. Options include:
Grain free, Z/D (from your vet), or Natural Ba***** *****mited Ingredient Diets, Nature's Variety Instincts line, Evo duck or venison, Nature's Variety Frozen Raw Medallions (I recommend that they be zapped in the microwave for 10-15 seconds on each side).
Personally, I think that if he's defecating right outside the box, this is still related to litter aversion or issues with his box rather than a medical issue but I wanted to provide other options for you to consider.
I hope this helps and provides various options to consider in trying to change this behavior. This is not an easy problem to solve, unfortunately, but I hope that by making a few changes, you will be successful. Deb