With the Olympic countdown ticking, human rights activists are turning up the pressure on Olympic sponsors. There are mounting calls to boycott the August opening ceremonies, publicly condemn the violence in Tibet and Darfur, and reroute the Olympic torch relay which is scheduled to run through Tibet – including all the way to the summit of Mount Everest in early May.

Activists calling for press and religious freedoms in China have re-doubled efforts to protest during the relay, in the wake of Beijing's crackdown on Tibetan unrest beginning March 14. They've marred the Olympic torch-lighting ceremony in Athens; tangled with security along the relay route in Istanbul (where activists of China's Turkic-speaking Uighur Muslim minority denounced a recent clampdown in their communities back home); and planned demonstrations when the torch passes through London, Paris and San Francisco in coming days. Pro-Tibet activists abseiled off Westminster Bridge with a giant protest banner, in anticipation of the torch's arrival in London (which is happening about now).

Actress Mia Farrow, who along with her organization Dream for Darfur has met with nine Olympic sponsors, is calling for consumers to switch off televised commercials during the Games and watch her live on the Internet from a Sudanese refugee camp. "There is one thing China now holds more dear than unfettered access to Sudanese oil and that's the successful staging of the 2008 Olympic Games," Farrow says in a new video posted on YouTube and subtitled in Chinese. "This desire has proven to be the lone point of leverage to a country that has proven to be impervious to all criticism."

Activists hope corporate sponsors -- big names like Coke, McDonald's, Kodak and GE – are more receptive. But they're growing increasingly frustrated. Tibetan activists say they are considering staging protests outside the offices of Olympic sponsors if the firms won't help reroute the torch relay away from Tibet. "We feel it would be an abhorrent sight to have the torch paraded by the Chinese government before a cowed and beaten population," says Matt Whitticase, a spokesman for the U.K.-based Free Tibet Campaign. "China has hijacked the torch for its own propaganda purposes and we're calling on the sponsors to defend the Olympic torch."

But Coke, one of three primary sponsors of the torch relay, turned down the Tibetan activists in an April 2 letter from CEO E. Neville Isdell, portions of which were obtained by Newsweek. "It would be an inappropriate role for a sponsor to comment on the political situation of individual nations," Isdell wrote, adding that the Beijing Games organizers and the International Olympic Committee selected the torch route, not the sponsors. "We believe dropping out of the torch relay or using the event to put political pressure on China would erode the ability of the Olympic Games to make a contribution to lasting change in China and its relationship to the rest of the world." The Tibetan activists' response: "He's obviously ducking responsibility," says Whitticase.

Mia Farrow also is unhappy with Coke. This week Dream for Darfur plans to issue a report card on individual Olympic sponsors’ responses to their campaign. Farrow has already signaled her assessment, however, after a meeting with Coke executives. On her personal web site, under the headline "Coke the Cowards,” she wrote an April 2 posting that said, "Shame on Coca Cola…the biggest brand on the planet has made it sickeningly clear that selling sugar water is more important than saving lives. Friends, hit them where it hurts - drink Pepsi!!"

Coke declined comment on Farrow's criticism, but noted that it has pledged $5 million over the next three years to help rebuild communities in Sudan; commited to reinvest profits earned there; and is giving $750,000 in Darfur relief aid to the International Red Cross. Other Olympic sponsors also are highlighting their humanitarian aid to Darfur. GE has pledged $4 million to groups like UNICEF and CARE. After talking with Farrow's group, UPS funded a $100,000 sustainable agriculture project in Chad, home to many Darfur refugees. The sponsors also met with China's special envoy to Sudan in a March 7 meeting arranged by the Beijing Games organizing committee. Sponsors say they are sharing concerns about Darfur with Beijing and the IOC.

Such efforts have yet to influence changes in sponsors’ elaborate and costly Olympic promotions, however. Marketing sources estimate that sponsors have paid up to $120 million each to underwrite the games. "We do not believe the Olympic Games should be politicized and used as a platform to influence the policies of sovereign governments," says Deirdre Latour, a spokeswoman for General Electric, which owns NBC, which will televise the games. GE also provided the solar lights for the softball fields and the rainwater recycling system for the Beijing's "Bird's Nest" stadium. "The Olympics are really the only platform we have left where all these countries walk in side-by-side. We believe the Olympics are a force for good."

Sponsors point to the International Olympic Committee (IOC) as the organization where protestors should take their concerns. "We believe any issues regarding the Olympics should be left to the governing bodies," says Lynnette McIntire, a spokeswoman for UPS, which provides logistics for the Games.

That’s not enough for activists who believe they will get farther with high-profile companies that are beholden to the whims of consumers than they will with the IOC. "The sense that I get from the corporate sponsors is that the IOC has not taken a leadership role and I agree," says Jill Savitt, executive director of Dream for Darfur. "I'm not sure who told China that shooting monks is a good PR strategy... The IOC is threatening to turn the brand of the Olympics into something as hollow as the rings."

Tibetan activists have already transformed the Olympic rings into a gruesome protest statement. A flash video on www.studentsforafreetibet.org opens with the official "Share the Dream" logo of the torch relay, featuring two silhouetted runners jointly holding the torch aloft beneath a red, swirling sky while jogging atop the rings. Suddenly, one of the runners dons a police cap and uses the torch to club the other runner - complete with grisly sound effects - into a bloody pulp. A stream of blood oozes out of the prone runner and drenches the rings in red. The swirling sky twists into a question mark: "Do you share this dream?" it asks. "We don't." Images like that are just the kind of counter-programming that give Olympic sponsors nightmares.