Abstract: In the first part of this talk, which is a sequel to my previous talk "Pitts Monads and a Lax Descent Theorem", I will begin by completing my exposition of the latter as follows. I will sketch the proof of the lax descent theorem and then briefly review the applications obtained. In the second part of this talk, I will introduce a notion of an 'equivariant Pitts monad' on a 2-category K (with bipullbacks and a pseudoterminal object T). Although not necessary for the general lax descent theorem, as we have shown, this stronger notion permits a certain passage from effective lax descent to effective descent. This passage will be illustrated in the case of the lower and upper powerlocale monads.