Tom's tuckboxes are fairly oversized, as are most it seems, so sleeved tiles should fit. I'm currently designing my own set of tuckboxes and the prototypes can fit inside Tom's boxes. I don't sleeve my tiles and prefer a tighter fit. I also have a tuckbox designed by Helen Holzgrafe and my prototype tuckbox fits inside it too. The other major tuckbox creator is Jamie Humphries, and his boxes are also generously sized.