Want to get away—all the way away? How about a week on a private island far off the grid, surrounded by sea, sand, and sky?

There is a whiff of redundancy about the term private island. The whole point of an island, surely, is that it's a little harder to get to and escape from than the average destination, because—and you might want to be sitting down for the conclusion of this sentence—it's surrounded by water. To some extent, therefore, one would think, every island is a little bit private by definition, and every island resident just a little bit special. As any Manhattanite will tell you. Or any Briton.

But perhaps this is just defensive pedantry from a man intimidated by a far more powerful connotation adhering to the term private island—that of madness. From Prospero in Shakespeare's Tempest to Marlon Brando as H. G. Wells's corpulent recluse in the 1996 version of The Island of Dr. Moreau (Brando himself had a 99-year lease on the Tahitian atoll of Tetiaroa), a private island is where you invariably end up when your radical views of how the world should be organized differently have (a) made participation in general society intolerable and (b) earned you the money to afford a private island. For as long as anyone can remember, no self-respecting Bond Villain or Mad Scientist has been without a fortified island, teeming with henchmen, from which to unleash his havoc on the world.

Yet, it would appear, all this is in the process of changing. With havoc fully established as the new natural condition of our continents, the last few years have seen a notable increase in the number of travelers seeking the solitude and serenity of the private island. Singly, in couples, or in corporate groups bent on brainstorming or team-building, more and more people are standing with their luggage on a beach, watching a motorboat or Jet Ski recede into nothingness, and being struck, all of a sudden, by the silence.

To Farhad Vladi, who over the last 30 years has established himself as the planet's preeminent broker of islands, this is good news. And no surprise. An island owner himself since the 1970's—and an aspiring one since boyhood—Vladi has always found the joys of island dwelling to be self-evident.

What no one ever appreciates, he tells me, is how much there is to do on a private island. The image of the castaway in tattered capri pants, scanning the horizon for dots for days on end, is a Hollywood myth, he assures me. More often, island renters find themselves gripped by a surging Teddy Roosevelt–like vigor that has them mounting proprietary expeditions into every corner of their new demesne, climbing trees for no reason, and at least toying with the idea of trying to kill something and eat it. "Mother Nature is the animator," Vladi explains. When the social buffer between oneself and the elements has been removed, apparently, "even rain can be exciting."

The close cousin of excitement, of course, is fear—which, in the private-island experience, can be dialed up or down at the customer's whim. Most rental islands come with at least a one-person support staff, armed with a cell phone and ready to step in the moment you break your leg or a killer robot escapes from your laboratory. But not all of them. The descriptions of some of the lower-end islands in Vladi's catalog sparkle conspicuously with creepy menace, such as Sleepy Cove island off the coast of Nova Scotia. A heavily wooded little chunk of rock in the shape of a human kidney, Sleepy Cove boasts "no staff and no caretaker present on the island to disturb you," but should trouble arise, "our management office in Halifax is only a phone call away." Which I seem to remember someone assuring Shelley Duvall in the opening scenes of The Shining.

Ultimately, though, it is surely the appeal of solitude that is driving the island-getaways business. As a recent, well-publicized study by psychologists at Duke and the University of Arizona pointed out, today's Americans are getting by with smaller spheres of acquaintances than at any prior point in the nation's history. It seems the average adult these days has only two true confidantes with whom to discuss his various gnawing malaises and biopsy apprehensions.

This trend has been evident in our vacationing styles for a while now. For the modern viewer, to look at one of those old iconic black-and-white photos of 10,000 people crammed ecstatically onto a postage stamp of beach at Coney Island or the Jersey Shore is to gaze into hell itself. There may indeed be a bit of redundancy in the term private island, but in this Googling, wiretapping, shower-camming age, can you ever have too much privacy?

Sleepy Cove, here we come.

Vladi Private Islands
A huge range of islands for rent and for sale.
902/423-3202; www.vladi-private-islands.de.

Private Islands Online
With more than 400 listings, an extensive and user-friendly resource for selling, buying, and renting islands.
647/477-5581; www.privateislandsonline.com.