(FORTUNE Magazine) - It's a good thing Sol Trujillo secured one of Australia's highest executive pay packages--about $8 million--when he signed on last year as CEO of its biggest company, Telstra (Research). At least he's being handsomely compensated for the personal attacks he has weathered since joining the government-controlled telephone company.

The former Orange and US West boss has become the foreigner Australians most delight in mocking. Cartoonists depict him in a sombrero astride a donkey, while shock jocks mimic an imagined Mexican accent, even though the Wyoming native's family came to the U.S. 200 years ago.

Trujillo's American management team--dubbed the "three amigos" in the press--are condemned by politicians for their obscene salaries and their inability to understand Australia. Sometimes the team hasn't helped its own cause: When right-hand man Phil Burgess remarked last September that he "wouldn't recommend Telstra shares to my mother," the stock fell 5% the following week. (Since Trujillo arrived in Sydney, the stock price has fallen 25%.)

Trujillo, 53, isn't fazed by the abuse or by the task confronting him. "The criticism doesn't change what we need to do," he says. "I've put the big UNDER CONSTRUCTION sign over the company. We need to take costs out--we need to change from being a regulatory-driven, public-service kind of culture."

Trujillo is betting big on broadband, signaling a $20 billion outlay over five years to extend access nationwide, bundling all services under a high-speed umbrella. "The first company that can step up and make all of today's devices work seamlessly is the company that's going to win the revenue," he says.

But there's stabilizing to do first, and fast. Telstra's profits were down 10.3%, to $1.5 billion, for the six-month period ended in December, despite a revenue rise of 2%, to $8.4 billion. The big bleeder is the company's fixed-line operation--expensive to maintain and accounting for about a third of revenues--which is quickly disappearing. "Local-call revenue has fallen 30% in the past two years," notes telecom analyst Ivor Ries of Melbourne brokerage E.L.&C. Baillieu.

Trujillo agrees: "There is a precipitous decline in fixed-line revenue, and broadband and wireless are barely compensating yet." But he says Telstra is "taking the medicine," planning to cut 25% of the current 45,000 workforce. "People have to understand that what they thought was there is not really there," he says.

The American is the latest in a succession of bosses who have come through the revolving door at Telstra, regarded as one of the world's toughest telco gigs. Says analyst Ries: "Everyone feels they own Telstra and thinks they have a right to a say about how it's run." And they do, from analysts to pensioners--expressing it with Aussie bluntness.

Telstra bosses are pilloried as ripoff fat cats when the company makes too much money, and for destroying household wealth when it doesn't. Bushmen demand services as sophisticated as big-city bankers, and neither group balks at assailing Telstra and politicians when they don't get it. With 85% penetration, Australia boasts one of the world's highest cellphone-usage levels. But Trujillo's recent move to uproot unused phone booths was met with rage from the few without mobile phones.

Negotiating Canberra's political minefield is tricky too. Trujillo has to placate 12 government ministries while answering to myriad parliamentary committees, each eager to score points. The government owns 51% of Telstra but is also its regulator, so it is compelled to grant Telstra's competitors cheap, unfettered access to the former monopoly's national backbone, much to Trujillo's chagrin. "I've seen this movie before at US West," he says of dealing with stubborn regulators.

A crucial part of Trujillo's brief is to prepare Telstra for "potentially the largest privatization ever"--a $25 billion offering that could hit international markets as early as September. "I would love for it to happen this year," Trujillo says. "It's always easier when you are under full private-market ownership--you don't spend as much time dealing with political interests. It's right for the government, it's right for Telstra, and it's right for Australia."

Canberra's current political climate seems as favorable as it can be. Says Baillieu's Ries: "The government wants to cure its Telstra headache as fast as it can." Prime Minister John Howard's pro-privatization government won control of both houses of Parliament a month after Trujillo was hired. That means sale approval will probably pass despite protests.

The privatization process, however, couldn't get much worse. About 1.6 million Australians own 49% of Telstra's shares, most of which are underwater, generating a grumpiness the government frets could translate into protest votes at election time. On March 17, Telstra was trading at $2.73, an eight-year low and half the $5.47 price when the government sold its last tranche in 1999.

Trujillo is determined to transform Telstra into one of the world's most advanced telephone companies. "This will be the next-generation company I've always wanted to build," he says. It's an ambitious plan, and there isn't much downside for Trujillo: If he fails, he can always go home and blame Australian rednecks and regulators for getting in his way.