Expatriation. As a golf pro, once he's expatriated and paid the exit tax (marking all assets to market and paying tax on the net appreciation), he can continue to come play in the US and, so long as he does most of his activities offshore - such as publicity, sponsorship, advertising, etc - the only portion of his income that will be subject to US tax - and then only at the rate of 30% for federal taxes - will be the actual purses he wins.
For individuals (and businesses) with the means, tax planning to minimize one's US taxes - without necessarily minimizing the income one earns that comes from the pockets of ordinary Americans - especially for people such as Mr. Mickelson who earn large sums of money from individual services over which they have a lot of control (i.e., not ordinary wage slaves or service industry workers), is quite feasible.
Basic choices can also be made by deciding whether to treat Mr. Mickelson as an employee - e.g., by setting up a corporation that actually makes the contracts for his services - or by deciding to treat his activities as the carrying on of his trade or business in the US. In the latter situation, his golf winnings would be income effectively connected with a US trade or business (so-called "ECI"), in which case he can deduct the expenses related to that income in determining his US tax liability. Again, however, so long as he remains a nonresident alien individual (i.e., not a citizen or greencard holder, and with less than 183 days of physical presence in the US), the only income subject to US tax would be his net ECI - meaning that, once again, the other income he earns from appearances and the like that he conducts offshore would remain free of US tax.
In fact, not only would a substantial portion of Mr. Mickelson's income from personal services become free of US tax, with just a little rejiggering all or substantially all of his investment income could become free of US tax - nonresident alien individuals who buy and sell securities in the US markets for their own account (i.e., they're not in the trade or business of buying and selling securities in the US markets) are not subject to US tax on their net gains, even if they make all of their gains from buying and selling the shares of American companies doing business solely in the US and selling primarily to US customers.
Remember the facebook founder who expatriated right after facebook went public? Just like that. There are going to be a lot of people - wealthy people - who will be expatriating solely for tax reasons. And as they expatriate, the tax base shrinks considerably.