Do your dreams revolve around places like Mustique, Fernando de Noronha, and Lord Howe Island? You have very good taste. These beautiful islands are exclusive, expensive, and incredibly discrete. Few people get to visit them. Even fewer have the chance to spend an entire vacation there. Here’s your opportunity to discover one of these islands in the Mediterranean Sea.

Cavallo, the only inhabited island in the Lavezzi Archipelago, sits in between Corsica and Sardinia in the Strait of Bonifacio. The privately owned island, nicknamed Île de Billionaires, is often tied to Corsica. It’s the southernmost point in France, and its ferry and rosé wine arrive from its neighbor to the north. But the island was first settled by the Romans, who sent prisoners to cut granite for their grand monuments on the mainland. Italian tourists even outnumber French ones during the busy season. But that doesn’t begin until July. Right now, you’ll have the 300-acre island practically to yourself.

When the ferry, which is only a 15-minute ride from Piantarella, pulls into Cavallo’s small port, you’re already in awe of the small island. Huge granite boulders, which look like they were borrowed from the Seychelles or the Baths in the British Virgin Islands, dot the coastline. Little white-sand beaches are tucked in between them. The air smells like myrtle, juniper, and, of course, salt. While traffic is practically nonexistent, as only bikes, golf carts, and electric cars are allowed. A golf cart from Hôtel & Spa des Pêcheurs is already awaiting your arrival.

Hôtel & Spa des Pêcheurs is a luxurious, seasonal hotel near Cavallo’s southern tip. The hotel sits on Shore Club Beach, which is known for its calm, clear water. Its simple rooms were built around the huge grey rocks; some of them are interesting interior design features. Balconies and terraces overlook the turquoise sea. So does the spa—where there’s a small indoor pool in front of a huge picture window and an open-air treatment room, so you can listen to the waves—and the always quiet pool.

After unpacking with the doors to your terrace wide open, your first stop is the beach, of course. At this time of day, its sand has a pinkish hue. Later, when the sun sets, it will start to look golden. It’s dotted with small shells, as well. But you’re more focused on the view. The huge boulders are even more impressive up close, especially contrasted by the gorgeous water around them.

Bar de la Plage is just a few steps from the beach. It serves salads and sandwiches with the same view. You order a caprese salad and a bottle of Sciacarello rosé wine. Sunset cocktails at the bar and dinner at nearby La Ferme will come later. While you have the rest of the week to beach hop, golf, scuba dive around shipwrecks and schools of barracudas, and gawk at the stunning mansions around the rest of the island. You may not be a billionaire—yet—but you certainly know how to vacation like one.