Hi there, I just sold my super dupa all in one top of the line weedeater and bought a $20 Black and decker and it is great. i use it one handed and its good for lawn touch ups and edging my flower bed and going around my benches in my yard etc.
It does need a cable though, i have a 100 ft one, but thats no big deal. this is so much easier to use than my old one, have a look i can recommend it:

http://www.amazon.com/Black-Decker-ST1000-Electric-Trimmer/dp/B000087R4E/ref=sr_1_2?ie=UTF8&s=hi&qid=1276113820&sr=8-2

By the way the string has a pretty small radius so i guess thats pretty ideal for you, plus you "feed" the line by just bumping it on the ground while it is switched on. good luck in your search.

Thanks Kevin,
But I really don't want to deal with a power cord.
Know of any good, reliable cordless ones?

The black and decker cordless trimmer looks decent but I second a corded trimmer if you have a small yard. My troy built electric was under $40, has auto line feed (non bump) and has a flip down edge guard to keep you from hitting flowers and stuff. It also has a plastic wheel for edging and is lightweight.

They do make small, cordless, electric mowers.

Here is a link that might be useful: Cordless Electric Mower