It was the kind of mistake that wage slaves can only dream of. Because of what the company called an “improper interpretation” of his employment contract, Sheldon G. Adelson, chairman, chief executive and treasurer of the Las Vegas Sands Corporation, received $3.6 million in salary and bonus last year, almost $1 million more than prescribed under the company’s performance plan.

Four more top executives of the Las Vegas Sands, which owns the Venetian Resort Hotel and Casino, received more than they should have. The total in excess bonus payments for the five men was $2.8 million.

The compensation committee of the board conceded that it had made an error. But it said that “the outstanding performance of the company in 2005” justified the extra money, and it allowed the executives to keep it.

Shareholders of Las Vegas Sands did not fare as well. The value of their holdings fell 18 percent last year.

As executive pay packages have rocketed in recent years, their defenders have contended that because most are tied to company performance, they are both earned and deserved. But as the Las Vegas Sands example shows, investors who plow through company filings often find that executive compensation exceeds the amounts allowed under the performance targets set by the directors.

Executives of companies as varied as Halliburton, the military contractor and oil services concern; Assurant, an insurance company; and Big Lots, a discount retailer, all received bonuses and other pay outside the performance parameters set by the boards of those companies.

It is the equivalent of moving the goalposts to shorten the field, compensation experts say.

“Lowering the hurdles is especially disconcerting because very often the goals are not set all that high to begin with,” said Lucian Bebchuk, professor at Harvard Law School and author with Jesse Fried of “Pay Without Performance.” Mr. Bebchuk said shareholders should be especially alert to increases in bonuses because more companies were shifting away from stock options and into cash incentives.

Some employment agreements actually stipulate that they will provide bonuses even if company performance declines. The agreement struck in 2004 by Peter Chernin, president and chief operating officer of the News Corporation, entitles him to a bonus even if earnings per share fall at the company. If earnings rise by 15 percent in any given year, Mr. Chernin’s bonus is $12.5 million. But if they fall 6.25 percent, Mr. Chernin’s bonus is $4.5 million, and an earnings decline of 14 percent translates to a $3.52 million bonus.

Last year, Mr. Chernin received $8.3 million in salary and $18.9 million in bonus pay. A company spokesman declined to comment on the bonus structure. He confirmed that the company’s chief executive, Rupert Murdoch, has a similar bonus arrangement. Company filings show that Mr. Murdoch received a bonus of $18.9 million last year.

While bonus and other incentive pay figures are included in company filings, shareholders hoping to calculate precisely what performance objectives executives must meet to receive such pay can be confounded.

Descriptions of bonus targets are typically vague and often include a laundry list of measures that the board may or may not consider. The board may factor in sales, earnings, stock price, capital expenditures, cash flow, even inventory levels. Company officials often explain the practice by saying that too-specific information on performance hurdles can give away corporate secrets or invite rival organizations to lure executives away by offering them contract terms that are easier to achieve.

Compensation experts counter that lists of vague hurdles may allow carefully chosen measurements to be met in both fair weather and foul.

Indeed, shareholders often find that the performance measures used by the company to determine pay can be very flexible. For example, Assurant, which is based in New York, says its compensation committee can adjust incentive payments for extraordinary events, “including, but not limited to, acquisitions or dispositions of businesses, litigation costs, tax or insurance recoveries or settlements, changes to accounting principles, asset impairment and restructuring.”

For bonuses paid in 2004, Assurant adjusted the earnings performance measure to exclude losses related to hurricanes along the Atlantic coastline. This adjustment helped to increase the company’s net operating income and therefore raised bonuses to the company’s executives in 2004.

It is impossible to pinpoint precisely how much the hurricane exclusion bolstered the Assurant executives’ bonuses in 2004. Company filings stated that without two exclusions, one of which was the hurricane impact, bonuses would have been equal to half of their target. Thanks to the adjustments, bonuses were paid at 1.72 times their target.

As James F. Reda, an independent compensation consultant in New York, pointed out, shareholders cannot adjust their results for things like hurricane losses, or losses on divestitures or discontinued operations, all of which deplete shareholder equity.

“What a lot of these plans are trying to look at is core business, and it is a decent argument,” Mr. Reda said. “But sometimes people get lazy and put all sorts of stuff in the restructuring bucket that don’t belong there — like operating expenses. Once you give management a little wiggle room, being smart people, they can figure out ways to take advantage of it.”

Often, company officials include everyday expenses — like those relating to sales and administration — in restructuring costs, making the company appear to be far more profitable.

In some cases, performance measures appear to reflect basic operational tasks expected of an executive, not something worthy of extra pay. Last year, Assurant’s compensation committee chose four elements to determine whether its executives deserved a bonus. Three were fairly typical financial measures: net operating income, revenue growth and return on equity at the company.

The fourth measure, though, was how well Assurant’s executives complied with Sarbanes-Oxley, the law enacted in 2002 after Enron and WorldCom collapsed. According to company filings, one-quarter of an executive’s bonus calculation related to his or her “compliance with Section 404 of the Sarbanes-Oxley Act,” a part of the law that relates to a company’s internal financial controls.

Last year, J. Kerry Clayton, Assurant’s chief executive; Robert B. Pollock, its president, and Lesley Silvester, an executive vice president, all received bonuses that were 1.62 times their targets.

The compensation committee of Assurant’s board is headed by Beth L. Bronner, chief marketing officer of Jim Beam Brands, a division of Fortune Brands. She is joined on the committee by Charles John Koch, vice chairman of the board of the Citizens Financial Group; Michele Coleman Mayes, general counsel for Pitney Bowes, and John M. Palms, president emeritus of the University of South Carolina.

Melissa Kivett, head of investor relations at Assurant, said that the hurricane exclusions in 2004 were appropriate. Because of a substantial increase in Assurant’s stock price, she said, “the compensation committee of our board felt that on this one occasion they needed to make an adjustment to net operating income to recognize and compensate management for this record performance.”

As for the bonuses relating to Sarbanes-Oxley, Ms. Kivett said they were designed “to ensure that we had all the processes in place to meet compliance goals. The result was we did have a clean SOX opinion.” She added that this year, the portion of the bonus related to Sarbanes-Oxley was smaller than it was in 2005.

But Paul Hodgson, senior research associate at the Corporate Library, an institutional research firm in Portland, Me., said paying a bonus for compliance with a law was unusual. “I can see making compliance a requirement,” he said. “Because they were not a public company until 2004 they didn’t have to comply with Sarbanes-Oxley before. But actually giving them a bonus for it is taking it a step further than my logic can let me go. Compliance with the law is part of your day-to-day work, not something you have to be incentivized for.”

Another company that gave extra pay to executives for regular business activities was Halliburton. Its top executives received special bonuses last year for settling asbestos litigation in which the company was a defendant.

Halliburton’s filings described the asbestos settlement as a “historical achievement” requiring a “tremendous amount of effort and sacrifices on the part of the employees who worked diligently over the last three years orchestrating and implementing this uniquely creative and complicated strategy.”

In recognition of their performance, the company paid cash bonuses totaling $5.5 million to 36 employees. Among them were C. Christopher Gaut, Halliburton’s chief financial officer; Albert O. Cornelison Jr., the company’s general counsel, and Mark A. McCollum, the chief accounting officer. Mr. Gaut received $750,000, Mr. Cornelison received $1 million and Mr. McCollum received $50,000.

David J. Lesar, the company’s chief executive, did not receive cash for his contribution to the asbestos settlement. He decided to take an option grant of 100,000 shares, worth $2.04 million at the time, as his extra pay for his settlement work.

Halliburton’s compensation committee is made up of Robert L. Crandall, former chief executive of AMR, the parent of American Airlines; Kenneth T. Derr, the committee’s chairman and a former chief executive of Chevron; W. R. Howell, a former chief executive of J. C. Penney; and Debra L. Reed, president of the San Diego Gas and Electric Company.

None of the directors returned phone calls seeking comment about the asbestos awards. Cathy Mann, a Halliburton spokeswoman, said: “This additional compensation was for the extraordinary amount of time and effort these individuals exerted, which was above and beyond what is normally expected of them in relation to their job responsibilities.”

At least Halliburton and Assurant produced strong returns to shareholders last year before handing over more to executives.

Perhaps most exasperating to shareholders are bonuses to executives who fail to meet their basic performance targets. Consider what was paid to Dan W. Matthias, chief executive of Mothers Work, a maternity retailer, and his wife, Rebecca C. Matthias, the company’s president.

According to the company’s filings, Mr. and Mrs. Matthias were not entitled to either a cash bonus or an option grant during the year because the company failed to achieve the expected growth in earnings before interest, taxes, depreciation and amortization.

Each of the Matthiases, though, received a grant of 40,000 stock options in fiscal 2005, on top of half-million-dollar salaries. The company’s compensation committee wanted to “recognize the progress made in the past year in both the development and launch of the company’s strategic business initiatives, which included its Destination Maternity superstores and expansion of the company’s relationship with Sears and a new tie with Kohl’s, another retailer,” its filing said.

“The compensation committee believes that the stock options grant is consistent with aligning the interests of these senior executives with the stockholders and will serve to reinforce the importance of improving stockholder value over the long term,” the filing said.

Those stock options, if they have not been cashed in, are now worth $2.8 million.

The compensation committee of Mothers Work is overseen by Joseph A. Goldblum, a private investor; David Schlessinger, founder of Five Below, a discount retailer; and William A. Schwartz Jr., chief executive of U.S. Vision, an optical products retailer.

A spokeswoman for Mothers Work said neither the company nor its directors would comment on the option grant.

“What is often missing in these after-the-fact changings of the bonus rules of engagement is a sufficient — or any — quid pro quo,” said Brian Foley, an independent compensation consultant in White Plains. Mr. Foley suggests that companies instead delay paying part of the bonus or stretch out the performance period to link the payout to an improvement in performance.

Like Mothers Work, Big Lots paid bonuses to executives last year even though performance was lagging. Big Lots, a discount retailer based in Columbus, Ohio, is going through a restructuring and last year hired a new chief executive, Steven S. Fishman. Performance criteria set by the compensation committee were not met, its proxy filing pointed out.

Still, four executives received one-time bonuses in 2005, on top of other pay. Brad A. Waite, executive vice president of Big Lots, received a bonus of $375,000; John C. Martin, also executive vice president, received $279,000; Lisa M. Bachmann, senior vice president, received $187,500, and Joe R. Cooper, chief financial officer, received $175,000.

As the Big Lots filing explained, without those one-time bonuses, the executives’ cash compensation would have been below the market average. The committee determined that the pay additions would not be excessive.

Big Lots’ shares started 2005 at $12.13 and ended the year at $12.01. Charles W. Haubiel, general counsel at Big Lots, said the bonuses were given to keep the company’s talent intact during a time of uncertainty. “The compensation committee identified a core group of executives,” he said, “and devised a retention program that said if you stay on during the year during the C.E.O. search process, you will receive a retention bonus equal to the target bonus you are typically eligible for.”

The compensation committee of Big Lots is headed by David T. Kollat, president of 22 Inc., a research consulting firm, who is also on the board of Wolverine World Wide, a shoe manufacturer, and Select Comfort, a maker of air-bed mattresses. The committee’s other members are Brenda J. Lauderback, a former president of the wholesale division of the Nine West Group, a shoe maker, who is also on the board of Wolverine Worldwide and Select Comfort; and Dennis P. Tishkoff, chief executive of the Drew Shoe Corporation.

These examples indicate that companies do not always practice what they preach about pay for performance. As a result, investors must read company proxies closely.

Back at the Las Vegas Sands, for example, the company’s regulatory filings say that executive bonuses will be paid only when they are earned. Bonuses are generated, the company said, “only upon the attainment of the applicable performance goals during the applicable performance period.” The compensation committee of the Las Vegas Sands’ board establishes both the goals and the period during which they are measured, the filings state.

Last year’s $2.8 million mistake proves otherwise, however. The mistaken payout was equal to almost 1 percent of the company’s earnings.

The unearned bonuses are notable not only because they followed $62 million in bonuses paid to the five men in 2004 (to reflect the “significant value” they created for shareholders when they helped secure financing for a mall at the Palazzo Hotel and Casino, adjacent to the Venetian). They are also striking because they cannot be justified as performance-based under the tax code. The extra bonuses therefore were not deductible as a business expense, making them more costly for shareholders.

The error did prompt a meeting on March 1 of the four-man compensation committee of Las Vegas Sands’ board, its filings stated. The committee considered what to do about the overpayments, and a majority concluded that the company’s performance supported them. One member of the committee dissented, the filing said: James L. Purcell, who retired as a partner at Paul, Weiss, Rifkind, Wharton & Garrison in 1999.

The members who voted to allow the executives to keep the unearned bonuses were Irwin Chafetz, a former executive at the Interface Group, a vacation tour operator that is owned by Mr. Adelson, Las Vegas Sands’ chief executive; Charles Forman, a former executive at the Interface Group who is chief executive officer of the Centric Events Group, a trade show and conference business; and Michael A. Leven, founder of U.S. Franchise Systems, franchisor of Microtel Inns and Suites. Even though Mr. Chafetz and Mr. Forman have extensive affiliations, either present or past, with Mr. Adelson’s Interface Group, they are considered independent directors according to New York Stock Exchange standards.

A company spokesman said that neither Mr. Purcell nor the other members of the compensation committee of Las Vegas Sands’ board would comment on the bonus overpayments. Las Vegas Sands officials who might be able to discuss the bonuses were traveling and unreachable, he said.

Mr. Foley, the independent compensation consultant, said he had never seen anything like the multimillion-dollar mistakes last year at Las Vegas Sands. “There’s nothing like playing by the house rules,” he said, “when you own the house, the chips, the rules and the croupiers.”