The link didn't work, I assume you mean these:
http://www.kallenshaanwoods.com/serv...n+Box+Examples
If so I don't think you would have to have 1 1/2 stock. 3/4 inch for the bottom and 3/8 for the top would probably do it. Here is a cool style of pen desk box made with 7/16 s stock...top and bottom if I remember what the maker told me.
Corey