Reply to Crappy Microphone - Getting rid of distortion

I have a really, really shitty microphone that I use to record myself every once in a while for a track. It's very sensitive to breathing/wind, etc... I was just wondering if there is anything that I could do in production to get rid of that annoying windy sound that appears. I've bugged around with filters and what not, but I can't seem to cover it up. Also, is there a technical term for this sound?