For oil based eggshell paint I have a lot of time for the dense black foam sleeves from Fat Hog or Wooster.
Fat Hog 4" fit on a simple bog standard mini roller / rad roller arm. Wooster 4.5" fit the Jumbo Koter frames.
The Fat hog is a convex end, which lets you get in really tight to edges. The Wooster is concave, and I find I use the end a lot to apply paint to mouldings
For water-based eggshell the 3/8" pile Wooster Pro Doo-z for skirtings and doors. I saw a video of an Arroworthy mini roller applying acrylic gloss on a pressed panel door. It seemed to go on and on and on.
Best ask Mark Nash about best roller sleeves for water-borne paint.