Printer Heads: How To Clean Without Wasting Ink

Hi Is there a way to clean printer heads from the outside, rather than allowing so much ink to be wasted by the machine blowing the ink through the heads to clean them. (This must be in a FAQ. I just need to be pointed to where this has been discussed a thousand times already.) A bit of background: I have an Epson CX6600 printer/scanner that has suddenly quit printing. The company sent the machine to me to replace an earlier model that developed the same problem. Maybe this machine has the same problem, or maybe it just needs head a more aggressive cleaning. I've "blown the jets" a few times, using over half the ink in the cartridges to do it, and the machine still barely leaves an image on the paper. (I keep a towel over my printers when I don't use them, and no one smokes in the house.) I'm hoping to avoid taking the time to crate and ship this machine as well. I'm not really interested in another replacement anyway. Thanks in advance for any help. Greg P.