Tim Cook got almost $400 million of restricted stock when he was named Apple chief executive in 2011, succeeding Steve Jobs. Regardless of whether Apple shareholders fared well or badly over the grant’s 10-year term, all Cook needed to do to collect that stock (worth about $700 million at today’s price) was keep his job. It was the kind of deal that pay mavens derisivelycall “pay for pulse.”

But two years later, Apple and Cook retroactively changed the terms of his grant, making about 40 percent of it “pay for performance” based on how Apple shares do relative to those of other companies in the Standard & Poor’s 500-stock index. Apple quoted Cook as saying he wanted to align his interests with those of regular shareholders.

What Apple didn’t say then — and now says only in passing — is that the change also gave the company a chance to get more than $200 million in tax deductions. Under Cook’s initial deal, Apple, which declined to comment, would have received no deductions because a 1993 tax law would have barred it from treating Cook’s grant as an operating expense.

By my estimate, revising the grant has generated $58 million in tax deductions so far for Apple, which would get $168 million more over the next six years if Cook receives the rest of his performance-based stock at today’s price. In return for agreeing to revise his deal, Cook has been collecting some restricted shares each year rather than having to wait until this Augustfor the first half of his grant and until 2021 for the balance.

The Apple change is an example of how U.S. companies, in the process of making shareholders happy by putting executives’ compensation at risk, have also managed to make an end-run around the 1993 law that was supposed to limit federal tax deductions on top officers’ compensation to $1 million a year per executive.

As Cook’s modified deal shows, those pay-deductibility limits are even more porous than we at The Washington Post and ProPublica realized three weeks ago, when we wrote that the deduction cap had failed to put the brakes on executive pay.

Under that 1993 law, “performance-based” compensation isn’t subject to the $1 million limit. The law, pushed by President Bill Clinton during his first term, initially covered five “named executive officers” at companies with publicly traded stock. Now, it covers four NEOs per company. (Chief financial officers were excluded in 2007).

Since we last visited the topic, we’ve learned more about how company compensation trends have changed, particularly in recent years. We had calculated, based on expert advice, that while executive compensation overall continued to skyrocket, the portion subject to the deduction cap had outpaced the pay-for-performance component. In fact, it turns out that the reverse is true. We learned this by hiring compensation data provider Equilar to tease out the details from proxy statements of 40 big companies, including Apple.

Those firms are the members of the “Nifty Fifty” club — the 50 S&P 500 companies with the greatest stock market value — that also disclosed executive compensation for 1992, the year before the limits on deductibility took effect.

Then, average total compensation per executive at the 40 companies was $2.1 million. In 2014, it had jumped to $12.7 million.

Along with aggressively boosting compensation, these companies have moved aggressively to pay-for-performance — so much so that 76 percent of the total compensation in 2014 was tax-deductible. That’s far more than if 1992 patterns had held.

The most striking number involves salaries, the only one of today’s pay categories that is totally subject to the deductibility limit. Salaries shrank from 23 percent of compensation in 1992 to a mere 8.8 percent in 2014. The biggest growth area: performance-based restricted stock, which made up 40.5 percent of 2014 compensation. Restricted stock made up only 9.7 percent of compensation in 1992, and little of it was performance-based.

“The trend has been to make restricted shares pay-for-performance instead of just vesting over time,” said Dan Marcec, Equilar’s director of content. He said 83 percent of restricted share grants to chief executives of S&P 500 companies are now based partly or entirely on performance, up from 58 percent in 2010.

Bonuses have also shifted substantially into the pay-for-performance category, Equilar’s numbers show. Bonuses made up 21.4 percent of executive compensation at the companies we reviewed in 2014, and 93 percent of that was performance-based.

What’s driving this shift? Tax deductions are a factor but not the single factor.

“There has been a lot of scrutiny and pressure from investors and from the say-on-pay rules that are part of Dodd-Frank,” Marcec said. That’s the financial-reform legislation that was passed after the 2008 financial crisis and that requires, among other things, that public companies offer shareholders a nonbinding vote at least once every three years on top execs’ pay packages.

Shareholders have been overwhelmingly receptive to “say on pay” proposals. According to a Conference Board study, 91 percent of the shares voted last year approved “say on pay.” Only about 1.5 percent of the firms in the Conference Board’s database — 44 of the Russell 3000 companies — failed to get support from a majority of the voting shares.

There is another development pushing performance-based compensation. The Securities and Exchange Commission will soon require companies to disclose the relationship between executive pay and companies’ performance. “This has been a major factor,” said Matteo Tonello, a Conference Board managing director.

The shift to performance-based compensation has greatly reduced whatever effect the 1993 deductibility limit may have had.

Some senators have called for the law to be amended to end pay-for-performance deductions. So has Hillary Clinton, who — ironically — is proposing to close a big loophole in one of her husband’s signature pieces of legislation.

There are no comprehensive numbers on what proportion of named executive officers’ compensation is tax-deductible. Steven Balsam, a professor at Temple University’s Fox School of Business, took a swing at the subject four years ago. In an oft-cited paper, “Taxes and Executive Compensation,” written for the Economic Policy Institute, he analyzed compensation paid by 7,248 companies in 2010.

However, to simplify things, Balsam counted all restricted stock and bonuses as subject to the deduction cap; we followed his method in our original analysis.

When I revisited the subject with him recently, Balsam told me that he couldn’t possibly do a detailed, company-by-company study of more than 7,000 firms. “There was no way to deal with it,” he said. “Even if you look company by company, it’s not clear what is deductible and what isn’t.”

In annual proxy statements, companies are required to provide a compensation summary and discussion, but the level of disclosure can vary greatly. And proxies generally note only that a company intends to comply with the deductibility rule, not whether it does.

Balsam’s explanation: "Even if companies think that they are making their grants deductible, that may not be the case. Companies have to jump through all sorts of hoops. The tax code is incredibly complex."

Which brings us back to the one restricted stock grant we decided to examine closely — Apple chief executive Cook’s.

One of the more interesting aspects of Cook’s revised deal is that it has no upside for him.

If Apple’s total return — stock price increases or decreases, plus reinvested dividends — is in the top third of companies in the S&P 500, Cook gets all that year’s performance-based shares. If Apple is in the middle third, he gets half of them. If it’s in the lowest third, he forfeits them.

Even if Apple produces extraordinary results, Cook won’t get more performance-based shares than his original grant gave him.

According to Apple filings, Cook forfeited stock then worth about $1.7 million in 2013, the first year his grant modification took effect.

However, Cook has already received about 2.2 million shares as the result of the modification, rather than having to wait until Aug. 24 of this year to get any stock at all. The cash dividends — currently $2.08 a share annually — on those shares exceed the $1.7 million value of the shares he forfeited. Under terms of his grant, as I read it, he doesn’t collect any dividends on unvested shares.

Companies, especially big companies, have been moving increasingly to performance-based compensation in an era in which they want to keep “say on pay” voters on their side. They also have to worry about so-called activist investors.

But there’s a fringe benefit. While loudly proclaiming their devotion to shareholder value, the companies can quietly take tax deductions that would not be available under “pay for pulse” compensation practices. It’s yet another example of corporate synergy — and tax avoidance — at work.