I finally sat down to make a decent partlet for my Italian dresses. That it, I've attempted it many, many times before, but they've all come out crap. This time around I achieved a way better result, after consulting all my online costume friends...
I used the same cotton as for the apron, and used fairly rectangular pieces. A small collar with box pleats was added, and in the front and under the arms there is / will be braided cotton cords with small fringe ends. It even fits! ;)