I have a Logitech G35 USB Headset, and had the very same problem Bertman did. I googled for a solution, and same up with much the same solution as cisneros, except I didn't use the model name in my file.
Here's my .asoundrc file:
You get the same result, though.
Note: This works for games too, like Quake I and Unreal Tournament 2004 (Both of which I play on occasion!)
Just thought I'd share this.