By JOANN S. LUBLIN

What a difference a year makes in the battle over executive pay.

Last year, Walt Disney Co. bowed to criticism from Institutional Shareholder Services Inc., the biggest proxy-advisory firm, by killing a controversial pay practice days before its annual meeting. This year, however, the media giant came out swinging.

Getty Images Disney CEO Robert Iger with Mickey Mouse at Disneyland in May.

ISS is "out of touch," Disney said in a regulatory filing March 1, after the proxy-advisory firm said CEO Robert Iger's performance didn't justify his compensation, valued at $31.4 million in the year ended Oct. 1. Disney said ISS "offhandedly and improperly dismissed the board's well considered judgment."

A showdown looms Tuesday, when Disney shareholders will again cast their annual-meeting ballots in a mandatory vote of confidence in the company's executive-pay practices. There will be a lot of people in investor relations departments cheering Disney on.

Companies have long locked horns with ISS, which advises investors like pension funds and mutual funds on corporate votes. But unease with the firm's ability to sway "say-on-pay" votes, which aren't binding but can be embarrassing for companies to lose, has kicked the antagonism up a notch.

Already, Disney's more aggressive stance seems to be having an effect. The California Public Employees' Retirement System will ignore ISS and support the media and entertainment giant's pay practices, an official of the biggest U.S. public pension fund said.

Calpers owns about 5.7 million Disney shares. A Disney spokeswoman declined further comment.

"Many companies are telling their pay story better,'' said Glenn Booraem, a principal of Vanguard Group Inc. He oversees its corporate governance program for U.S. investments worth more than $800 billion.

Many money managers have long followed ISS's recommendations on shareholder proposals, director elections and other ballot issues, which can be a problem for companies now that a 2010 financial overhaul law requires them to conduct regular votes on executive pay.

Companies complain ISS has a stranglehold on how performance-related pay is judged. ISS rejects the criticism. "There is not a monolithic group of investors following one proxy adviser,'' says Carol Bowie, the advisory firm's head of research for the Americas.

But the firm's advice does carry a lot of weight. On average, a negative ISS recommendation influences between 13.6% and 20.6% of votes cast on management proposals, according to a study published in the journal Financial Management. And ISS has made a lot of negative recommendations on pay, advising investors to oppose 11% of roughly 3,300 say-on-pay votes during 2011, according to Ms. Bowie.

In response, companies have begun lobbying investors aggressively with challenges to ISS's assessments and alternative ways of measuring how CEO pay is tied to performance. About 100 companies challenged negative ISS recommendations last year, estimated James D. C. Barrall, an executive-pay specialist at law firm Latham & Watkins LLP. He said he wouldn't be surprised "to see at least twice as many challenges in 2012, given the emerging battle over different ways to measure the alignment between pay and performance.''

At Disney, ISS dropped its 2011 negative recommendation after the company decided to eliminate "gross-up" provisions in employment agreements for Mr. Iger and three fellow executives. Under those provisions, the company would have paid taxes on payments due the executives if they lost their jobs following an acquisition. Disney's say-on-pay vote received support from 77% of votes cast last year.

Qualcomm Inc. tried fighting ISS this year, with mixed results. The semiconductor company's CEO, Paul Jacobs, received $21.7 million in total compensation in the year ended Sept. 25, as his stock awards more than doubled to $14.3 million.

ISS recommended a "no" vote, saying the pay was high compared with Qualcomm's peers. Qualcomm lashed back in a Feb. 21 filing, saying ISS "fails to recognize our unique business structure'' and wrongly compared Mr. Jacobs's package to companies with similar revenue rather than market capitalization.

ISS spokesman Ted Allen defended the methodology, saying revenue "is a widely accepted measure of a company's complexity and management challenges.''

Qualcomm won approval of its pay practices at the March 6 annual meeting. But the margin of victory—at nearly 69%—fell from nearly 95% last year. A Qualcomm spokeswoman declined to comment.

Another common gambit is for companies to try to take investors' attention away from the potential value of stock or options awards at the time an executive receives them. ISS focuses on that figure, which is what companies have to report under Securities and Exchange Commission rules.

Now, more companies are pairing those figures with "realized pay" or "realizable pay''—calculations that purport to do a better job of reflecting what executives actually take home.

The approach "can only decrease the impact of ISS," said Charles G. Tharp, CEO of the Center on Executive Compensation, a business lobbying group.

Write to Joann S. Lublin at joann.lublin@wsj.com

A version of this article appeared Mar. 13, 2012, on page B3 in some U.S. editions of The Wall Street Journal, with the headline: Disney Takes On Proxy Adviser.