any suggestion for a narrow mini receiver

What about the Boston Acoustics Recepter Radio® HD? This unit is 4" high, 7" wide and 6" deep. I have one in my bedroom and it is very good. It include a clock and preset for both AM and FM stations. Please see:
http://www.bostonacoustics.com/whats_new.asp

I think Musical Fidelity makes some very narrow equipment. I think it is the
X-series. I haven't heard it but I do own one other piece of their gear (the Tri Vista SACD player) and it sounds just great.

The Sharp Newbie mentions is the best "cheap" deal going right now, plus it contains a CD player.

However, it is a bit wider than 13".

The CD/amp sections are nice. FM is OK for background music with the supplied antenna. AM is not so hot.

I'm in LA. The tuner's sound quality will vary with local, antenna/signal quality.

The Musical Fidelity X-series are great, but not that cheap, and it's not made anymore, so you have to settle for secondhand. I think, reconsidering this threat, I would go for the Teac Reference series, since it's pretty good, and you can buy new components to adjust the system to your needs (surround etc.).

Depending on how much high the shelf is, and your need for speakers, etc, the inexpensive Tivoli Audio stuff (Kloss design) might fit the bill. I'm thinking about some for an office system, but have only had the chance to hear it in a store under less than optimal conditions. It gets good reviews, but wonder what 'Goners think.