One of the joys of cruising is that it enables us to visit extraordinary places, places we may not have even heard of were we not cruising: places like Selvagem Grande, the largest of Portugal’s Ilhas Selvagens, or Savage Islands: population two humans, one dog and 40,000 very noisy seabirds.

This tiny island—or is it just a large rock?—lies in the Atlantic Ocean between Madeira (autonomous territory of Portugal) and the Canary Islands (Spain), at a longitude that makes it an ideal stop for migratory birds. Hence its status as home to the world’s largest colony of Cory’s Shearwater, a magnificent seabird that breeds along rocky cliffs in the Mediterranean Sea, the Azores and here, Selvagem Grande, a strategic dot on a migratory map.

When we arrived on our Valiant 40, Moon River, the newborn Shearwater chicks were still tucked up in their nests, waiting for flight feathers to emerge, while their squawking parents commuted back and forth on fishing trips. Only a handful of yachts visit here each summer—you need prior permission from the authorities back in Madeira—so when a battered RIB first approached us, I supposed he was coming to check our papers. But the warden, Manuel, had a more pressing concern: “Will you join us for dinner?”

When Adele, our daughters Zephyr and Looli, and I clambered ashore, the human population shot up 200 percent. Chief warden Manuel Jose Jesus and his scientist colleague Hanny live in a cozy house at the head of the island’s single decent anchorage where they work for Portugal’s natural parks department.

They relish visitors. Upon arrival, Manuel and his faithful pooch, Selvagem, took us on a tour of the island’s cliff-top paths, where we saw legions of comically fluffy Shearwater chicks in cave-like nests hidden among the rocks. Cute they were, but Manuel warned: “If you put your hand in there they’ll attack, and that beak can cut you. It’s like a knife.”

Allegedly, Cory’s Shearwaters are silent in flight, but here on Selvagem Grande, you never would have guessed it. Manuel said the constant cries of the adult Shearwaters can drive you crazy. But each fall, when the Shearwaters migrate south with their newly grown-up chicks, the loneliness is worse.

“Sometimes we’re annoyed with them because of the noise when we want to sleep and we can’t. But when they’re not here, we feel strange,” the quiet-spoken former soldier told us.

Supplies, along with a new shift of wardens, arrive every three weeks aboard a Portuguese navy vessel. Although the wardens have satellite television and have just been given a phone, I could see how the vastness of the surrounding sky and Atlantic Ocean could become overwhelming. Capt. Kidd is said to have buried treasure in a suitably mysterious looking cave eating into the base of one of Selvagem Grande’s cliffs.

Still, in spite of the constant racket and the overwhelming destitution, the Selvagens are a source of international contention. Portugal’s big neighbor, Spain, covets the islands, which are much closer to the Spanish-ruled Canaries than to Madeira. The fight is not so much over the barren specks themselves, but the fact that they give Portugal a presence so deep into the Atlantic, greatly expanding the country’s Exclusive Economic Zone.

At the heart of the debate is whether the Selvagens are islands or just rocks, in which case they’d cease to count as territory, instantly shrinking Portugal’s zone. According to the United National Convention on the Law of the Sea, “Rocks which cannot sustain human habitation or economic life of their own shall have no exclusive economic zone or continental shelf.” Human habituation is a shaky prospect here, as abandoned stone ruins in the interior attest.

However, Manuel and Hanny’s dinner diplomacy put another spin on the issue.

That night, seated around a table with a huge steaming pot of pasta, the Atlantic roared around and stars seemed to fall to our feet. Wild cries in the darkness reminded us that the Shearwaters’ epic story was still unfolding. And a deepening of the echo of waves as they rumbled into sea caves around the anchorage warned us that the wind was shifting. We clinked bottles of Sagres beer, joked about Portugal’s spat with Spain, and heard Manuel’s lifelong dream to visit New York. Long the lights burned on Selvagen Grande, a pinprick in the Atlantic vastness, yet truly an island of human warmth and generosity—our island refuge, whatever the lawyers eventually declare.