Sometimes, when I’m out walking with my seven-year-old shepherd mutt, Peggy, we’ll pass a young family. Peggy will pant lovingly in their direction, and the kids will wave or come in for a pet or two. When we part ways, I often hear the same loud whisper spoken from child to parent: That dog has three legs!

While this is very much true, it’s also not immediately apparent. Though Peggy’s pec and back muscles have bulked out since her accident, she walks with only a slight lilt, and when she runs—as she often does, in pursuit of her one true love, Ball—she’s figured out how to reach approximately the same speeds of her four-legged days.

My partner and I found eight-week-old Peggy via a rescue organization, and we named her for Peggy Olson, my favorite character from Mad Men. For the first weeks of her life, she bounced from one end to the other of our Brooklyn apartment, explored the streets with her dog-walking buddies, and generally lived a happy New York life. But when she was two, we moved to Montana—in part for work, in part out of exhaustion with the city—and Peggy’s glory days truly began. She gleefully fetched balls in the chilly waters of the Clark Fork River, tromped through feet of snow, and reveled in the miles of off-leash trails that wind through the Missoula foothills. And she chased many, many deer—which is how, one afternoon while with her dog sitter, she was hit by a car and eventually lost her back right leg.

No, it’s not the life I imagined for Peggy. It’s better.

At first, I was bereft. Our vet assured us that dogs adapt quickly, but my dreams of weeklong backpacking trips, complete with Peggy hauling her own food in a cute little dog pack, had evapor-ated. But while she was recuperating, I realized I was mourning a rather limited understanding of a dog’s life. As we’d spend afternoons in the backyard, surrounded by towering ponderosa pines, it became clear that Peggy was no longer interested in the deer passing through. She just wanted to sit, observe, and sniff. Unlike me, she’d figured out how to be satisfied with her new reality.

Now, in our new home on Washington’s Lummi Island, Peggy has only become more hilariously stubborn in her ways. If you don’t let her spend a solid two minutes sniffing the otter’s nightly tracks across the road, she’ll lay down and refuse to go any further. She likes broccoli ends but not celery; pizzles but not rawhides. Most of all, she prefers to lay on our deck, stare at the blue herons feasting at the shore, and follow the sun, her ears perked to the sounds of the gulls and eagles and loons. After about three miles on a trail, her back leg starts to get weak, but she still gallops in her slightly off-kilter way. And when it dumped a solid three feet of snow this winter, she insisted on being the one to break trail.

No, it’s not the life I imagined for Peggy. It’s better.

—Anne Helen Petersen writes the cultural commentary newsletter Culture Study.