Do you know for sure you're susceptible? A common myth about altitude sickness is that fitness (or lack thereof) is the major factor. It's one detail, but plenty of very fit people get it anyway. It's all about your limits. Whatever they are, push them, and you're in trouble.
There are plenty of other things you can do that help. Avoiding excessive caffeine and alcohol is another. I've heard that antacid tablets (taken before you start your hike) can help but that seems to be in the "may help" category...
The longer you give yourself to acclimate the lower your chances of getting it. Try to get in early but also slowly. Don't head straight up to 12,000' in your first few hours if you've never spent time there before. Also, if you're REALLY worried, a can or two of "sport oxygen" is super light and provides immediate (though short) relief.