Locals nicknamed her Alex and feverishly debated the whale’s gender for weeks. Finally, scientists performed DNA tests on pieces of dead skin pulled from the water and determined that Alex was short for Alexandra. Though many had hoped she was pregnant–this would guarantee regular whale visits, since they often return to the waters where they were born–Steve Burnell of the National Parks and Wildlife Service guesses that she’s too young to calve. Alex is probably in town, Burnell said, to recover from a small injury to her tail, most likely caused by tangling with a rope or a cookie-cutter shark. She is en route to Antarctica, where southern rights live, after wintering in the warmer waters off the Australian coast.

Alex’s visit, say environmental experts, is a good sign for whale populations. “It shows that ending hunting [in Australian waters] was definitely the right way to go,” says Denise Boyd, an oceans campaigner for Greenpeace. The group has seized this opportunity to launch an online petition to end whale hunting around the world.

Alex is also a swimming adverstisement for how much cleaner Sydney Harbor has become. Last year the state government launched a $60 million campaign to stop rain from washing litter, chemicals and waste into the water; industry along the harbor is now tightly controlled. Says John Dengate of the Environment Protection Authority, “Alex is the latest in an increasingly long line of critters turning up in the harbor,” including oysters and native water rats, last seen 70 years ago. “There’s still a long way to go, but we’re going in the right direction,” he says. “The animals seem to agree.”

So does the public. The National Parks and Wildlife Service has had to work overtime, baby-sitting Alex to make sure no one gets too close to the whale. Basil Evans, 71, managed to sneak through the defense. As he approached Alex in his dinghy, the whale suddenly lifted her huge head out of the water just meters away. “I still break out in a sweat thinking about it,” said Evans. “She was 10 stories high.”