Any day now, Jumby Bay Island is going to be the best private island in the whole wide world, says Frédéric Vidal. He should know. He is master of Jumby, the 300-acre Caribbean island, a seven-minute luxury boat ride from Antigua. Jumby is owned by over 30 investors, who all have sensational residences on the island—and one’s for sale (thanks to a pending divorce) for US$35 million. Villas and bedrooms are also in the 54-key Jumby Bay hotel portfolio, all managed by Oetker Collection.

It helps when deeming anything as “the best” to know what you’re talking about. Vidal has typical French style, paired with the rare experience of running royal palaces for one of the Middle East’s top royalty. He also, today, has owners who do want the best.

But what actually makes a private island, and what makes one the best? First, it has got to be an island. Secondly, it needs to be private to a certain degree—the public cannot just turn up and wander over it. Of course, there are other famous private islands. Consider Isla Secas in Panama, which can accommodate a total of 34 in various casitas—there are luxury tents, as well. The whole island is owned by New York-based Louis Bacon, founding CEO of Moore Capital Management and renowned conservationist and philanthropist. He’s also the financial brains behind New Mexico’s Taos Ski Valley, population 66.

Eternal heartthrob Marlon Brando craved privacy to such a degree that in 1962, when filming Mutiny on the Bounty in French Polynesia, he bought the entire atoll of Tetiarøa, 35 miles from Tahiti. The atoll has 16 islands, some seemingly as prehistoric as the beginning of history. Only one island is inhabited, and this holds the eponymous 47-villa The Brando. All villas have private plunge pools, and food is overseen by France’s current top toque, Jean Imbert, who’s also to be found at Hôtel Plaza Athénée in Paris.

The Brando is, by the way, far ahead on the sustainability front, partly because of its seawater air-conditioning system, SWAC. It also hosts eight full-time scientists working on islands and one of the joys of staying at The Brando is curated excursions to neighbouring islands to learn about crabs and so much ecological else. Think the Galapagos without the iguanas. Another thing about private islands is the joy, generally, of getting there. In the case of The Brando, you jump on the resort’s own private airline, Tetiarøa Air, from Tahiti.

North Island, in the Seychelles, is best reached by a 15-minute helicopter hop from Mahé airport. The island is probably still best known worldwide for the numbers of royalty who have honeymooned there, and for ecology. It has 11 villas, including one 8,000-square-foot supremo. One of North Island’s great attractions is watching its giant, three-foot-long tortoises, Aldabrachelys Gigantea, some well over a hundred years old (they seem to love lumbering at slow snail’s pace across the chopper landing spot).

Privacy is a word that comes up again and again in the context of private islands. In the Maldives, many islands have just one resort on them, but Four Seasons Private Island Maldives at Voavah is among the most exclusive—only 22 people, ideal for family or small group buyouts. Belize offers the seven-villa Cayo Espanto, three miles off its coast. Off the southeast coast of Africa, a 20-minute boat trip from the Zanzibar mainland, there’s &Beyond’s 10-villa Mnemba Island Lodge, for whale-watching and studying dolphin, green turtles, and the magnificent bird life. Alternatively, think Fiji’s 240-acre Matangi Island—with nine adult-only villas and, arguably, the three best treehouses on a private island.