The brand is Sunpack (from best buy) My UV filter is a hair over 5mm tall, the CPL is 8. I cut an 8mm thick strip of tape and taped it around the edge of the UV, you for sure get vignetting at 11. Goes away by 13mm.
I suppose if you can find a sub 5mm tall CPL it would work, but I'm not sure where you will find that.
And Trevor, haha.