I have a lovely Thayer Deck Switch Tray that I recently acquired. However, you cannot use a normal boxed deck of cards with it!?! A normal deck of cards is too thick (they measure about 15mm thick) so the flap sticks up slightly--but noticeably. It really doesn't work well with a loose deck of cards either. So, is there a thinner deck of cards (including the box) that anyone can suggest. The boxed deck needs to be about 3mm thinner for the flap to lie flat.

'Blue Cohorts' are supposed to be a thinner cardstock, might do the trick, but not sure if the box is significantly smaller