Activated charcoal added to a well balanced recipe.
I use a high lard recipe with some coconut and 5 % castor. Also some palm and even a touch of olive or rice bran.
Even though it's a soap for acne I do not use a very high cleansing number. Odly enough a high cleansing number makes the skin go into overdrive in the oil production and the acne gets worse.
That's because it strips the skin of natural oils, so the body thinks the skin is not getting enough oils, so over-produces oil to compensate. That's why even though I have a tad bit of oily skin, I use a moisturizer every day. If I skip it, my skin gets oilier because my body thinks my skin is not producing enough oils.
(I know I'm not explaining this exactly correct, but this is how it was explained to me by my dermatologist when I was a teenager a LOOOOONG time ago)
I researched what each oil, fat or butter would bring to my recipe. When I was satisfied with my basic soap recipe, I then added skin friendly essential oils and activated charcoal. It takes a bit of research, but it is worth the effort. I have to say, that I do not use lard in a soap recipe for acne.