What about 83(b) elections? http://www.startuplawblog.com/section-83b/
I may (probably) be wrong, but I believe 83(b) can only be used if your company allows you to exercise early before your options have vested. To quote from that link (emphasis from the article):
[…] Section 83(b) election generally cannot be made with respect to the receipt of a private company stock option. You must exercise the option first and acquire the stock before you can make a Section 83(b) election, and you would only make a Section 83(b) election in that instance if you exercised the option and acquired unvested stock (if the stock acquired on exercise of the stock option was vested, there would be no reason to make a Section 83(b) election).
Not all companies allow you to exercise early, so if you have to wait out your vesting cycle the 83(b) isn’t helpful and you’re back to square one with the AMT (or equivalent in your country).
This applies, albeit less urgently, for stock grants at publicly traded companies, too. In general, though, I strongly recommend that people in this situation just pay for an hour or two with a pro (probably a tax attorney) before making any decisions with tax consequences.