One of the many interesting structures described in John Becker's Pattern and Loom (long out of print but now available as a pdf download) is Han qi, an ancient weave popularly known as Han damask. Han qi is a one warp, one weft structure that combines plain weave with 3/1 straight twill. The Becker book has an excellent explanation of how the cloth is designed, and clear diagrams of the Han dynasty looms on which it was originally woven. Refer to pages 21-41.
I've played with the structure from time to time, and just this week wove a small sample for an upcoming Photoshop workshop. This sample is woven on a straight threading on a 40-shaft dobby loom, (click to enlarge) but with other patterning the structure could also be woven on 4 shafts with supplementary heddles.
The optimum sett is one in which the warp is slightly denser than the weft, although a balanced weave also works with many materials. I've successfully woven Han qi on a jacquard loom, and also on a dobby with a networked threading (4-end initial).
As with any damask, the cloth works well in monochrome, but contrasting warp and weft can also be interesting. As you may have guessed, the reverse side features 1/3 twill and plain weave.
Correction: The pdf version of the book is slightly different from my physical copy. The page reference are correct if you have the 1987 edition, but if you are looking at the download version (second edition), refer to pages 16-33.