Investor concerns about hydraulic fracturing at Chevron have eased, in contrast to a slight rise at rival Exxon, as the two largest U.S. oil companies faced growing pressure at shareholder meetings to name independent chairmen to improve governance.

Groups of protesters descended on the respective annual meetings in California and Texas.

One of about 80 outside Chevron headquarters in San Ramon waved a sign that said "Fracking is environmental rape," while others called on the company to better address its protracted legal battle in South America over oil pollution.

Energy companies use hydraulic fracturing, or fracking, to create fissures in rock like shale that allow oil and gas to escape. In the process water, sand and chemicals are pumped at very high pressures into wells drilled deep into the ground.

"If you think the reputational risks are bad with people coming from Ecuador, wait until they come from Pennsylvania and Colorado," said Larry Fahn, president of investor pressure group As You Sow, while arguing for a Chevron shareholder proposal on the risks of hydraulic fracturing.

Yet concerns about the oil and gas production practice among shareholders were notably more subdued. After a similar fracking resolution at the 2011 meeting had support from a surprisingly high 41% of Chevron shareholders, a similar proposal got 27% backing this year.

Support among Exxon Mobil shareholders for such a resolution rose to just under 30% from 28% last year.

There was also a Chevron resolution on appointing a board director with environmental expertise, but an early vote count showed 23% supported it, down from 25% last year.

Activists had seized on the resolution as a sign of investor discontent with Chevron's handling of a hotly contested $18 billion verdict against it in Ecuador. The proposal was even backed by the advisory firm Institutional Shareholder Services.

Canadian lawsuit

On Wednesday, plaintiffs in the case filed a lawsuit in the Superior Court of Justice in Ontario, Canada in an attempt to enforce the verdict and seek to obtain Chevron's assets in Canada.

In a statement, Chevron said it would defend any enforcement action, adding, "if the plaintiffs' lawyers believed in the integrity of their judgment, they would be seeking enforcement in the United States - where Chevron Corporation resides."

Chevron Chief Executive John Watson, speaking to reporters after the meeting, said the amount of evidence assembled by his company's lawyers casting doubt on the Ecuador case meant it was no longer a "he said, she said" story.

Watson acknowledged concerns about fracking being safely done were "fair game" and Chevron wanted to address the issue in conversations with local communities and their advocates.

"It's not clear to me what additional information (needs) to be disclosed," he added.

Watson also serves as chairman of Chevron's board, and a proposal on giving that job to someone independent received support from 38% of shareholders. Support for an independent chairman of Exxon rose to 35% from 31% a year ago.

Exxon shareholders, who gathered in Dallas, threw more support behind the executive compensation package after the world's largest publicly traded oil company made an effort to seek more input on the matter.

That effort appeared to pay off: 78% of shareholders cast a non-binding vote in favor of compensation for the executives, up from 67% last year.

Exxon CEO Rex Tillerson's total compensation rose 20% in 2011 to $34.9 million, a year when the company's stock price was up 16% and profit grew 35%.

About 25 protesters gathered outside the meeting, holding signs that included: "Exxon Loves Millionaires."

Tillerson said the company, the largest U.S. producer of natural gas, was contemplating gas exports from Canada and the U.S. Gulf Coast because supplies were more than enough to meet demand. Natural gas prices have hit their lowest in a decade.

Asked about the potential for Chevron exporting natural gas from the United States, Watson said the company had taken a look at it, but was not interested at this time.