So a friend sent a link to an article in The Daily Mail that included a large photo of a menu for the wedding of two people who just got married (who they are really, really doesn't matter). The friend sent the link because the photo was an example of an affliction all letterpress printers must battle when doing jobs for graphic designers: the demand for "deep" impression, often on paper as thick & soft as coaster board.
Note how lousy this printing looks. The letters are pushed so deep into the paper that the impression actually distracts from reading. It's so deep that, from this image, you can't even be sure if the darker outer edges of long lines are shadows caused by the depth of the impression, or the tell-tale over-inking of a printer who didn't bother with, or know about, basic makeready.
Graphic designers: do not demand deep impression from your printers. If they're any good, it will break their hearts to print that way. The result simply tells the world you don't know anything about letterpress printing. The right amount of impression is a function of the type, the paper and the form. (No impression also is BS, a remnant from letterpress' later commercial days when offset was in its ascendancy.) Letterpress requires some impression, but not so much that it qualifies as debossing.