If you use a 10 speed set up with double rings and you can get the largest sprocket to work on the large chainring and the 12 (or 11 if that is your thing!) sprocket to work on the inner ring, then putting a single ring on should work as it will be better than either of the two previous extremes. There may be some bad mechanical losses in the system though! This sounds very much off topic, now that I have read it back to myself. Appologise!
Martin Coopland, Scotland.