Howdy! Just thought I’d share the way I like to store small sheets of veneer (for marquetry) 

I’ve seen people use presses but they don’t work for sheets of different size (as mine are). 

So what I do is stack them in decreasing size, lay them on a flat panel that’s slightly larger than the largest one (here a chopping board cause it was just the right size). Then I put them in a vacuum storage bag, and suck the air out. 

This holds them all flat, protects the delicate edges and prevents them getting mouldy or too dry.