My friends and I constantly discuss impression in letterpress. Specifically, when deep impression is TOO deep.
In letterpress, the most important thing has always been a good, even impression. Letterpress purists will insist upon leaving nothing but a "kiss" impression, barely any impression at all. In fact, if you were to see this type of printing, which I've done while learning letterpress, it would be hard to distinguish it from offset printing except for the paper used. Deep impression, letterpress instructors may tell you, is a sign of bad printing because it renders the opposite side of the paper useless for printing or anything else.
The deep impression that letterpress is able to provide, however, adds a very tactile quality to the printing and gives it an artisan flair. And since letterpress is such a labor-intensive affair, it needs the artisan quality in order to remain competitive with newer, less labor intensive (and therefore cheaper) techniques.
Too deep of an impression, however, which is often seen in letterpress, not only adds a reverse wording braille like emboss to the back of the paper, rendering that side useless, but since paper only has so much give, we've also seen it crease and fold the paper where the too deep impression exists.
It becomes a balance then, to give an impression deep enough to satisfy today's market's tastes, but light enough to leave the opposite side useable if printing a notecard or business card or the like. I think this is actually going to be the new mark of a good letterpress printer -- to know how to vary impression to the use of the final product.