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Between washing your thumbs and scrubbing your palm creases with your fingertips, you should also wash your wrists, at least a hands-width down your arms. Total time from "Give us this day our daily bread" through "Holy Mary, Mother of God," including your wrists, should be about 25 seconds. And your hands should be wet and soapy for that entire 25 seconds. I'd do an alcohol-based hand rub the same way. It's the combination of friction and either soap and water or alcohol-based hand sanitizer that actually gets rid of the germs.
Finally, once you're done, don't touch the bathroom faucet or door with your hands. Use a dry paper towel. It's almost certain that those surfaces have been contaminated by some person who washed their hands inadequately, or not at all.
