What are some relatively low-cost ideas for dampening background noise for home recordings w/o soundproofing?

I am attempting to record some songs I'd like to try to market, but the background noise is disgustingly present. I've tried noise filters and either they don't work well enough or they work, but the voices you WANT to hear fall victim to digital distortion. I've learned I can quiet the hum of the computer fan pretty effectively by throwing a towel over it (though not for too long - don't want it to overheat). Are there any relatively simple, low-cost ways of resolving this?