i had some african mahogany boards that were pretzel shaped so i came up with a small project to use them. i ripped the boards so that i had strips of rift sawn and strips of flat sawn. the rift sawn was turned into the sides and top and the less attractive flat was the bottom.
found a nice straight grained piece for the drawer front.
the back - the top section you see is crossgrain glued but its maybe 1.5 inches. there is a floating panel in so its not glued the entire height. pine drawer sides.
one thing i forget (repeatedly) when using thin stock / small boxes is that the drawer ends up having a similar mass to the case. even if its a smooth action, the case can move. i should have made the bottom 4/4 to beef up the mass.
second item shown is a tissue box that i've made about 60 times in different forms.
trying plan for movement and to give it a seamless look i used veneer the top over mdf or plywood, and miter all 4 sides. the top of the sides would be mitered. it lined up perfectly about 20% of the time. I've since changed to creating homemade plywood. in this case, 3 ply, all scraps from the zebra wood. then i put it into a shallow rabbet.
then if my box isn't square, who cares. i use a shooting board to fit it to the opening.
i've stopped adding hidden splines as well. just overkill and adds a lot of complication. with the top glued in, its plenty sturdy.