I've never used potassium soap - perhaps you meant and insecticidal soap? What I use for anything such as spider mites, thrips, aphids or whiteflies is either Dr. Zymes Eliminator or some Spinosad.... they're both organic and can be used at any stage of the plants growth right up to the day of harvest.... and they will kill not only the adult insects but the eggs and larvae as well.... For insects/bugs that chew leaves (as opposed to sucking on them) like catepillars and whatnot, I use BT (bascillius thuringeneisis) .... Always spray just before lights out so you don't burn the leaves in the light...
Good luck...