I stumbled across the Sony 135 F2.8 [T4.5] STF other day.
I have read through the review but I can't for the life of me figure out what the twin-aperture setup is supposed to do!
Basically there is a manual iris that is designed to produce as round an opening as possible in order to render out of focus highlights as circles (instead of pentagons, or octagons etc.)
Since the whole purpose of this lens is to produce smoother blurred backgrounds using the apodizaion element, it would be a waste if the effect were ruined by not having a circular aperture when stopping down slightly.
Presumably having this aperture stop right down would compromise it's roundness, so they added a second aperture which can close all the way down for when you want a very narrow aperture.
From the article: