How wide can you go? There are several rectangular vitreous china sinks on overstock that have reviews that say they fit in an 18" deep vanity:

Here is a link that might be useful: undermounts at overstock

Thanks for the link. I have found two sinks I think may work:

Porcher 12100-00.001 Marquee Petite Rectangle Undercounter Lavatory - White
http://www.faucetdepot.com/prod/Porcher-12100-00.001-Marquee-Petite-Rectangle-Undercounter-Lavatory---White-124575.asp#.UGHSEVFP8ge

and

Courtyard White Undermount Lavatory Sink
http://www.overstock.com/Home-Garden/Courtyard-White-Undermount-Lavatory-Sink/2677720/product.html

Has anyone used either one?

Since you will have very little space between the back of the faucet and the wall (or backsplash), you may want to use a drain stopper that is not connected to the faucet.

This means you can remove the pull-up handle/knob from the backside of the faucet. I'm not sure what that type of stopper is called, but it operates totally separate from the faucet....same as a kitchen faucet and drain stopper.

Umbrella drains are probably the most popular right now.

BTW, mamattorney, faucetdirect has the Porcher right now for $147.50 plus an additional 3% off. (There are also a couple of pics of it installed in the reviews there.)

We have the Porcher 12100-00.001 Marquee Petite Rectangle Undercounter Lavatory - White in all of our bathrooms. The sink is lovely, but quite small. I wouldn't use this sink if I were to build the bathroom from scratch, but it does work on a small, narrow countertop. FYI - that sink is no longer available in the Porcher line. I've spent 2 weeks looking for one since we need one more. The brand was merged and is now called DXV: https://www.dxv.com/product/pop-petite-rectangle-undermount-bathroom-sink-by-dxv

PlumbTile can order and ship it as well as various showrooms. They had the best price so far ($189)

Nantucket UM-16x11-W.