Tim is right. There isn't much else you can do really. The mic goes straight into your computer via USB, so there's no adjustments to be made on that end. Audition is a powerful DAW, and should do everything you need to do. You might try a little bit of compression to help with your volume issues (just don't go overboard). I can't remember if Audition supports real-time effects or not. If it does, throw a compressor (I believe AA3 comes with an Izotope compressor even) in your mic channel and play with it until the volume evens out. Otherwise, do everything you can to use good mic technique and improve your recording space. The closet can sound like a little echo chamber if it is too small or left untreated. Leaving clothes in for density is a good idea, assuming you can fit inside with them. Small spaces are easier to control, in theory, but they are also harder, in that quick reflections are a nightmare. A bigger room helps disperse some of those immediate reflections. Basically, you'll have to keep trying.
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Gear: Digidesign 003R / Telos Zephyr XStream ISDN codec / JK Audio Broadcast Host digital phone hybrid
PC: HP 6005 Pro MT PC running Windows 7 Pro 64-bit w 3 GHz AMD Phenom II x3 B7, 4GB RAM
DAWs: Sound Forge 10 Pro, Vegas Pro 9, Adobe Audition 3.0, Pro Tools LE 8.04, Reaper x64.