Gulant's recommendation is to disclose everything to the U.S. government, even if the accounts or structure were not set up to duck taxes.
"You're not going to be able to hide this stuff forever," he said.
He also recommends that clients don't set up overseas accounts as mechanisms to reduce their tax exposure, even if the structure would arguably be legal.
"It's just not worth the headache, in my view, that comes with this stuff," Gulant said. "It's being carefully watched, it's being systematically shut down."
Getting some people to reveal their overseas accounts or shell corporations isn't always easy.
"From my experience, the people that are involved with these things, they're not bad people," Gulant said. "But the old paradigm is this is what wealthy people did, this is what you do to hide your taxes."
"We've had people who have shown up at the office and go through their portfolio of assets, and we'll advise them what the penalty is going to be" if they don't disclose the accounts to the government, or pay taxes on them, Gulant said. "And then we never hear from them again," he said with a laugh.
In other cases,he said, "we've had people who have continued to engage in a series of schemes, if you will, against our advice or judgment, and some of them have actually paid the price ... civil and criminal."
Gulant said that post-Panama Papers he expects some wealthy people to continue tax reduction strategies, which can include "strategies with off-shore trusts."
"There are some legitimate trust structures that can be utilized," he said. "But you have to be very careful, because if you don't do it right, you could put yourself in a situation where the tax situation is worse."
Sometimes, he said, the rich throw that kind of caution to the winds and set up an offshore asset protection trust in a place such as the Marshall Islands or the Cook Islands, which offer both a tax-free environment and privacy about who actually is controlling the trust.
Those people think "I'm going to transfer all these assets to an island somewhere in the Pacific and my creditors, including the IRS are not going to be able to get it," Gulant said. But that belief won't necessarily withstand the legal power of the U.S. government.
Another potential legal strategy — even in the face of tightened rules about such inversions — is to move an existing company overseas to a country that has a lower corporate tax rate than the United States, he said.
And Americans can renounce their citizenship to avoid U.S. taxes. In 2015, nearly 4,300 Americans gave up their citizenship, an increase of more than 20 percent, the third year in a row for the record to be broken.
Individuals who are willing to do so can also move within the United States to reduce, often greatly, their annual tax hit.
David Tepper, the hedge fund billionaire who founded Appaloosa Management, filed to move his personal tax residency in December from New Jersey to Florida. He also officially moved Appaloosa out of New Jersey to Miami in January.
Both moves could save Tepper hundreds of millions of dollars in taxes, since Florida has no income taxes, unlike New Jersey, where the top income tax rate is 8.97 percent. People close to Tepper told CNBC he made the move to be closer to his mother and sister, who live in Florida.