After reading posts by a number of forum members, I bought a DeWalt Cordless Router(DCW600B). It works well but I found that if I used a 5Ahr battery it was too top heavy so I wound up using a smaller battery. I've only used it for doing round overs so the smaller battery has been fine.
The one thing that surprised me is that it has a "quick stop" feature - when you turn the router off, the bit stops immediately. That's a nice feature.
I'm not going to sell all my corded trim routers but this one is very nice. Thanks to everyone who recommended it.
Mike