You can do letterpress on handmade, Asian paper! Despite its thin countenance, Japanese papers can hold their own against the letterpress machine. Simply set your pressure higher as you press and the letters and/or images come out as they would on your usual Western paper, except with a unique surface that comes only from these special papers made from wood-free (bast) fibers.
Above is an extra heavy weight white Kozo paper (M-0207-#3) with a letterpress image, made by Lois Harada, a graduate student at RISD- (Rhode Island School of Design). Remember that even though this sheet is extra heavy weight, it doesn’t need to be- It’s stronger than it looks. Kozo paper, in particular, has more wet-strength than a cotton paper. Below are some images of instructor Dan Wood’s April 2010 letterpress course at RISD.