OF THE WORLD'S 36 SPECIES OF WILD CATS, none has a more powerful bite than the jaguar. Its skull, wide like a cinder block and wrapped with muscle, is engineered to crush. Its snout, short and compact, generates enough leverage to crack a tortoise shell like an egg.

With these tools, the jaguar has perfected a devastating method of dispatch: the cranium crunch. Wrapping its jaws around its prey's head—in some cases nearly as large as its own—the cat drives its two-inch canines through more than half an inch of bone to puncture the brain. On other occasions, a jaguar pierces the skull through the ear canal, leaving no visible entry wound.

Until recently, the mechanics of a jaguar's bite were little more to me than an academic abstraction. That changed quickly when I visited a Bolivian animal-rescue organization called Comunidad Inti Wara Yassi (CIWY). CIWY rescues wild animals like monkeys, birds, pumas, and jaguars from Bolivia's black market; the animals might come from abusive situations or well-intentioned people who simply can't care for them. One of CIWY's goals is to rehabilitate the animals and, when possible, to release some of them within the park. But that's not done with the big cats, in part because of the potentially severe consequences of a mishap.

A handful of Bolivians steer this ark with the help of international volunteers, and to make the cats' life sentences more enjoyable, the organization promotes a practice called "direct contact." For six to ten hours a day, live-in volunteers—many of whom have no more expertise with animals than what they've gleaned from a family dog and Animal Planet—walk these predatory felines on a leash through the jungle. For the next 11 days, I will, too.

Shortly after arriving at Parque Ambue Ari, CIWY's 1,991-acre jungle compound in the central-Bolivian department of Santa Cruz, I am assigned to Jaguarupi. His name is derived from an indigenous word that means "little jaguar"—the same ironic humor that lends itself to 300-pound bouncers nicknamed Tiny.

"Rupi" came to Ambue Ari from a private residence as a cub in 2003, soon after the park opened, and now he's the biggest cat on the block, a 260-pound alpha male. At least two volunteers work with Rupi, so after signing a waiver stating that jaguar wrangling "leads to an inherent risk of injury or accident," I'm paired with 23-year-old Adir Michaeli, who's one month into a three-month stay and therefore our team expert. With a sturdy chin and thick black eyebrows, Michaeli looks like an Israeli Colin Farrell. Having spent four years as an explosives specialist in the Israel Defense Forces, he has chosen jaguar walking as his method of relaxation.

On our way to Rupi's cage, Michaeli launches into a safety briefing: Don't touch the jaguar. Don't yank on his leash. When he jumps you, don't fight back, as it will only encourage him (and you won't win). Never turn your back on him. Try not to let go of the leash. Don't let him smell your fear. And don't ever, ever forget: He could kill us both in seconds. Have fun.

I am now qualified to walk a jaguar.