Tips to getting low notes on an Alto Saxophone out?

I play an Alto Saxophone in Band. I used to play the Tenor, but due to lack of Alto's, I had to switch back. My Alto isn't in perfect shape, and my reed probably isn't the best "#" for my specific model of Alto (not sure exactly what model it is), so both of those might contribute to my troubles playing lower notes, even below "G". I've heard about raising the Saxophone off of a support to allow the reed to vibrate more, and I'm already using a lot of air - any more would blast out the notes. One song that we are working on demands a low C-Sharp to be played very soft/quiet-like, and that's pretty much impossible for me. Any tips?