Many of the strategies for avoiding the AMT are not really reducing the AMT but rather increasing the regular tax. One example is not claiming miscellaneous itemized deductions. Other strategies involve shifting the tax burden from one year to the next (such as delaying your last real estate tax payment or estimated state income tax payment or other non-AMT deductible items into the next tax year) or shifting income earlier (e.g., redeeming savings bonds, realizing short-term capital gains, trying to get a bonus paid earlier).
The AMT works by adding back in various deductions and income exclusions. So avoiding the AMT means reducing those factors. But that's just increasing your tax to hit the AMT, not reducing the AMT. The only real benefit is when you can shift enough of those items to another year so that neither year will be subject to the AMT (i.e., spreading out the items more evenly or shifting the non-AMT deductions into a year with higher income). But often this is beyond the taxpayer's control -- you can't shift nondiscretionary medical expenses from one year to the next.
The AMT can be really annoying. I bought a hybrid vehicle a few years ago but lost the tax credit because of the AMT. I was counting on the tax credit to help defray the higher cost of the hybrid.
If you are subject to the AMT, focus on increasing charitable deductions. They are worth more to you under the AMT than under the regular income tax.