Romping around one's very own private island in the sun -- what a delightful vacation prospect. Away from the crowds and the clamor, the beach and the sea are yours alone. Well, almost yours alone.

Dotted across the world's seas and oceans are a number of resorts on small tropical islands, luxury retreats from a high-pressured world, catering to travelers who want to get away from (almost) everybody else. Some islands -- among them Palm Island and Petit St. Vincent in the Caribbean Sea -- are so tiny they can be circled on foot in less than an hour.

What sets these hideaways apart from other island hotels, aside from their diminutive size?

Each resort sits alone (or nearly alone) on its own tiny island except for the surf and the sand and the waving tropical foliage. And the number of guests is sharply limited. If you are not really all alone, at least the illusion is that you are. On Palm and Petit St. Vincent, the whole island is the resort: no roads, no traffic and very few people, just lots of nature. Take a walk and the only people you meet are other guests, hotel staff members or passing yachters ashore for dinner or a drink. The beach is often yours entirely.

A handful of resorts in the Caribbean qualifies, and others are found in the Fiji and Tahitian islands of the South Pacific and down the Great Barrier Reef off the northeast coast of Australia. Not all are convenient to reach, but their remoteness appeals to adventurous travelers.

Most are quite comfortable places, even luxurious despite their isolation, featuring a special kind of personal service. On Turtle Island in Fiji, let the staff know on which empty beach you will be sunning, and at lunch a waiter will arrive by boat with chilled lobster salad and champagne.

"Roughing it, in comfort," writes one guidebook author.

These hideaways, not surprisingly, tend to be expensive. One of the costliest is Long Island, a new 300-acre holiday island off the coast of Antigua in the Caribbean, where the winter high-season rates are $425 a day per couple. However, this includes all meals, most recreational activities and several extras, such as complimentary laundry service and even postage stamps for your post cards.

Some have an unusual history. Palm Island, for example, was leased 18 years ago by the grateful government of the West Indies to seafarer John Caldwell, an American who had cruised the Grenadine Islands on his charter schooner planting thousands of coconut palms. With a hired crew of West Indians, Caldwell and his wife built their luxury retreat on Palm's 110 acres, limiting the accommodations to about two dozen sea-front bungalows and several private villas.

Indolence on these islands is catered to. Reading and napping may be the major activities. Shaded hammocks, big enough for two, hang from thatched shelters spotted along the beach at Petit St. Vincent. Another Caribbean resort in the British Virgin Islands tantalizes: "Come to Peter Island and do what you've always wanted to do. Nothing."

Of course, most also provide a full program of water and other sports activities: snorkeling, scuba diving, board sailing, deep-sea fishing, day-long yacht cruises.

Don't expect much organized entertainment, except for an island steel-drum band one or two nights a week. In the evening, guests usually gather for cocktails and dinner in the fashion of a private house party. Afterward, the before-bed choice is conversation, a cordial at the bar, card games or a walk on the beach beneath the stars.

As one guest at Lizard Island on the Great Barrier Reef recalls her stay: "I snorkled, I drank beer and I went to sleep early. It was wonderful."

Among the small hideaways that come closest to anyone's dream of the unhurried, uncrowded life on a private island:

*PALM ISLAND BEACH CLUB, St. Vincent, Grenadines. What delights you immediately are the brilliantly blue sea and white sandy beaches that define Palm. The water is agreeably warm, wonderfully clear and calm, perfect for simply floating lazily under the sun.

Just a few yards up from the shore, under a grove of palms, is an open-air bar. When the sun gets too hot, you can find shade here and a wide variety of cooling rum punches. It is hard to image a more ideal way to spend a day at the beach, and one fine day follows another at Palm.

For more active guests, instruction is offered in snorkeling, scuba diving, water skiing, sailing and board sailing.

The Caldwells are both experienced sailors. He once set sail alone from Panama to Australia, but after four months at sea his 29-foot boat was lost its mast in a storm and he drifted for 49 days until landing in Fiji. Later the couple captained charter cruises through the Grenadines.

Yachts or charter ships frequently sail up to Casuarina Beach, the principal anchorage. The crew and passengers swim ashore for an hour or two at the bar, bringing a splash of social life, especially welcome if too much solitude has become wearying. Once a week a large cruise ship, the Sun Princess, arrives, and then Casuarina bustles for a day.

But four other beaches, and more privacy, can be found on a walk around Palm's mile-and-a-half perimeter. The island is basically round and flat, except for a couple of stumpy green knobs that rise like toy mountains from this miniature land.

Lodging is in 24 comfortable bungalows or in private villas scattered under John Caldwell's palms at Casuarina Beach. Afternoon tea is served on the bungalow patios, and other meals are taken in the open-air dining room. The menu features many local creole dishes -- all very informal.

In the Caribbean, the weather tends to vary little from season to season. But winter is when resorts fill fastest and prices jump. The pace and the rates are more relaxed during the summer.

Palm once was called Prune Island, and that name can still be found on some maps. To get to the resort, guests must fly to Union Island (via Barbados) and then board Palm Island's launch for the 10-minute ride to Palm. Many of the resort's staff commute from Union. Rates: High season, Dec. 15-April 14, $220 per day for two, including meals and afternoon tea; low season, April 15-Dec. 14, $175 per day.

For more information: John Caldwell, Palm Island Beach Club, St. Vincent, West Indies, (809) 458-4804.

*PETIT ST. VINCENT RESORT, St. Vincent, Grenadines. The American manager and part-owner of this deluxe resort, Hazen K. Richardson, also captained a passenger schooner in the Grenadines before purchasing his island in the mid-'60s. At the time, it was uninhabited except for wild goats scampering over its small hills.

Now little trams, driven by the attentive staff, scamper over pathways delivering snacks or drinks to the two-dozen secluded cottages, built attractively of local stone. The tram service is something of a trademark for the elegant but relaxed 113-acre island resort.

About every 20 minutes or so, one of the trams drives by each bungalow. If you want a drink from the bar, you raise a flag on the bungalow's flagstaff and place a message in a bamboo mailbox outside your gate. Next time around, the tram driver places your order on a shelf at the gate and rings a little hanging bell. If you happen to be sunbathing in the nude, nobody knows. Some guests, says the management, don't put on clothes until it's time for dinner.

The bar and dining room are in an open-air pavilion on a hillside overlooking Petit St. Vincent's lovely harbor. Chartered yachts anchor frequently, and "Jump Up" night, when there's dancing to a West Indian steel drum band, can get quite lively.

Petit St. Vincent is just south of Palm Island. To reach it, guests must also fly to Union Island and then board the resort's boat for a 30-minute ride to the island. Rates: High season, Christmas and Jan. 26-March 17, $400 a day for two, including meals and all facilities; low season, Nov. 3-Dec. 20 and April 15-Aug. 31, $220 a day for two; shoulder season, $340 a day for two.

For more information: P.O. Box 12506, Cincinnati, Ohio 45212, (513) 242-1333.

*LONG ISLAND RESORT, Antigua, West Indies. The resort, just off the north coast of Antigua, is new, having opened only last December. But the claim is that Christopher Columbus himself named it back in 1493. In years past, Long Island was a sugar plantation.

Last season lodging was in 12 cottages at the Estate House, a 200-year-old rebuilt Spanish colonial mansion with a traditional red-tile roof. Most of the cottages are suites with separate sitting rooms and private patios overlooking the Caribbean. A wide, gracious veranda offering shade and a fine view sweeps around the main building.

This year an additional 16 rooms are being added in a villa near Jumby Bay Beach, just a few steps from the water along a 500-yard stretch of white sand. Several of the rooms will feature private shower courtyards that let you imagine you are bathing out-of-doors.

At another beach, Pasture Bay, the coral reefs are said to be particularly good for snorkeling. Hiking, running and cycling trails thread through the white cedar and loblolly woods between the beaches. The island can be circled on foot in about two hours, about a 2 1/2-mile walk.

Access to Long Island is by the resort's launch, a 15-minute ride from Antigua. You are offered a rum punch when you step aboard. Rates: High season, Dec. 21-April 15, $425 a day per couple, including three meals, cocktails, house wine; low season, June 1-Sept. 3, $250 a day per couple; shoulder season, Oct. 15-Dec. 20 and April 16-May 31, $300 a day per couple.

For more information: Resorts Management Inc., The Carriage House, 201 1/2 E. 29th St., New York, N.Y. 10016, (800) 225-4255.

*PETER ISLAND HOTEL AND YACHT HARBOUR CLUB, British Virgin Islands. The island is 1,050 acres, and this low-keyed luxury resort occupies 650 of them. The rest is mostly undeveloped. Currently, there are 32 rooms in eight "harbour houses," of Scandinavian design. The front decks look out toward the harbor.

But 20 more rooms in five two-story villas are being added at Deadman Bay Beach. These, too, will feature exotic bathrooms, each with an indoor tropical garden and a large window looking out toward the palms.

Two private villas can also be rented. The swankest is the scenically situated Crow's Nest -- four bedrooms, four baths, a private pool and use of a 46-foot yacht -- at a cost of $1,500 a day for eight guests (meals included, of course).

The terrain on Peter is quite hilly, climbing to above 500 feet. The island's three beaches are Deadman Bay, a one-mile crescent of white sand near the resort's lodging; the more-secluded White Bay across the island, and Reef Bay, adjacent to Deadman, where the shell collectors head.

Besides water sports, there are horseback riding, guided trail rides, and day cruises to the U.S. Virgin Islands.

Peter Island is reached by the resort's yacht from Tortola. Rates: Until Dec. 14, $195 a day for two, including breakfast and dinner. Beginning Dec. 15, from $325 to $395 daily for two. Packages for longer stays offered.

For more information: Peter Island, 220 Lyon St., Grand Rapids, Mich., 49503, (800) 346-4451.

*YOUNG ISLAND, St. Vincent. Young Island is just a dot, 20 acres of it, about 200 yards off the south shore of St. Vincent. With only 24 cottages, it offers the exclusiveness of a private island but the proximity of a major island, if exploring is what you have in mind.

Small as it is, Young has its own satellite island, Ft. Duvernette (The Rock Fort). At the top of this knobby perch are the remains of an old fort, and grand views of the Grenadines. It is the setting for an occasional evening cocktail party and barbeque.

All water sports are available, and a yacht is anchored off the small beach for cruises.

Young Island is reached by ferry from St. Vincent. Rates: High season, Dec. 20 through March, beginning at $270 a day for two, including two meals. Until December, $155 a day for two.

For more information: Ralph Locke, 315 E. 72nd St., New York, N.Y. 10021, (800) 223-1108.

*MERIDIAN CLUB, Pine Cay, Turks & Caicos Islands, British West Indies. Located between the Bahamas and Haiti, Pine Cay is a beautiful 800-acre island owned by about 20 property-holders, some of whose homes are available for rent, as are 12 comfortable bungalows at the Meridian Club.

The bungalows, with their own patios, are linked by flowered trellises to the club's Main House. The Main House features an open-air dining room, where dinners are served family style. In the evening, guests gather upstairs for dessert and coffee, and to watch the sunset.

Guests have full run of the island, which includes a wonderful 2 1/2-mile long beach, where there is plenty of privacy, as well as excellent shell collecting. A full range of water sports is offered along with opportunities to explore the many neighboring islands.

Pine Cay is reached by Cayman Airways from Miami or on scheduled charters from Ft. Lauderdale, all arriving at Providenciales (Provo) in the Turks & Caicos Islands. It's a short hop by Pine Cay inter-island charter to the resort, where there is a "packed-sand" airstrip. Rates: High season, Dec. 16-April 15, $260 a day for two for a bungalow, including meals; low season, Nov. 1-Dec. 15 and April 16-Aug. 1, $225 a day for two.

For more information: Pine Cay's Meridian Club, P.O. Box 350367, Ft. Lauderdale, Fla. 33335, (800) 327-3139.

*TURTLE ISLAND LODGE, Fiji. This is the island on which the teen romance "Blue Lagoon" starring Brooke Shields was filmed. The lagoon, indeed, is very blue.

"Turtle" is the tourist name; to Fijians it's Nanuya Levu. It is owned by an American, Richard Evanson, who sold his San Francisco business to travel the world. He stopped in Fiji when he saw the 500-acre Turtle Island and its 12 white-sand beaches, small mountains and tropical valleys.

It is a very private place, about 100 miles northwest of Fiji's main island of Viti Levu in the Yasawa island group. You get there by scheduled seaplane service, Turtle Airways, from Nadi's International Airport (on Viti Levu). There are accommodations for only 20 guests in 10 bures, the island-style hand-built thatch houses. While the temperature is pleasant year-round in the Fiji Islands, the chance of rain is greatest from December through May.

"My island," writes Evanson, who arrived in 1972, "is on a volcanic lagoon two miles across, surrounded by seven islands, four of which are uninhabited. On the three inhabited islands live my neighbors, some 400 Fijians . . . Fijians have to be the friendliest, most fun-loving, easiest-going people on this planet."

Meals feature lobsters and other seafood caught in surrounding waters. Quail, duck and chickens are raised on the island, and mangos, papayas, coconuts and other tropical foods grow plentifully. Rates: $280 a day for two, which includes meals, all drinks (in each bure the bar is stocked daily to your request) and all sports and entertainment activities.

For more information: C.C. Evanson, 12706 E. Evergreen, Vancouver, Wash. 98664, (206) 892-8423.

*KAINA VILLAGE, Manihi, in the Tuamotu Archipelago of French Polynesia. Manihi is a small, barely inhabited atoll (population about 300) about 310 miles northeast of Papeete, Tahiti. Its one tourist hotel, the new Kaina Village, recently built by the Climat de France chain, accommodates about 32 guests in 16 Tahitian-style thatch bungalows.

The bungalows are located right over the water and are reached by gangways. Some mornings, you can hear the small fish splashing beneath the floor. A short ladder from each terrace leads directly into the lagoon, which makes a before-breakfast swim ever so easy.

On this small island there is actually a sightseeing attraction: a black pearl farm, which is open to visitors. The beaches are beautiful white sand, and a full program of water activities is available. Rates: $153 per day for two, including meals.

The Tahitian weather generally is pleasant year-round. The warmer rainy season is from December through February; from March through November, the climate is cooler and drier.

Manihi is reached by three flights a week from Faaa airport at Papeete, about a one-hour-and-40-minute trip with one stop.

For more information: Climat de France, 1601 N. Kent St., Suite 1101, Rosslyn, Va. 22202, (800) 2-FRANCE or (703) 527-5410.

*HIDEAWAY RESORT, BEDARRA ISLAND, the Great Barrier Reef, Australia. Only about three miles off the east coast of Australia, Bedarra is nevertheless a very private retreat. On about 200 acres, it offers only 14 comfortable bungalows all but hidden in a green tropical rain forest of bamboo and, sometimes, wild orchids.

"The 'full' sign goes up when we have 28 guests," says the owner, Trans Australia Airlines. The Australian Tourist Commission describes Bedarra as "an oasis of untouched beauty," washed by the Coral Sea and the South Pacific.

Like similar islands in the area, Bedarra provides access to the Great Barrier Reef, reputed to be the largest expanse of living coral reefs in the world, with more than 1,500 kinds of fish and 400 species of coral. Many Australian outfitters arrange from one-day to two-week scuba-diving, snorkeling and game-fishing trips for visitors. The most-pleasant season is April to September or October; the least-agreeable months, January and February.

Bedarra is circled by eight warm-water beachs, but there's also a swimming pool, positioned, it is said, "to catch the sunset over the sea." Flights from Townsville (45 minutes) or Cairns (30 minutes) on the mainland land at nearby Dunk Island, and transfer to Bedarra is by launch. Rates: About $130 a day per person (double occupancy), including all meals.

For more information: SO/PAC, 1448 15th St., Suite 105, Santa Monica, Calif. 90404, (800) 472-5015.

*LIZARD ISLAND LODGE, the Great Barrier Reef, Australia. At 2,500 acres, the island is a bit larger than the others, but most of it has been set aside as an Australian national park. The lodge, resembling an Australian pioneer homestead with veranda, accommodates only 30 guests in 15 stylish bungalows.

Set in a blue lagoon, Lizard has 24 sandy coves, in this case almost one per guest. They can be explored on foot or in small outboard motorboats. "Only the seagulls and the terns and perhaps the rare osprey will note you arrive for your picnic in one of our little motorboats," says the management. "Only their footprints are on the beach."

The island is at the northern end of the Great Barrier Reef in a region that has become famous for big-game fishing, particularly black marlin of record size. The marlin season is from August to December.

The resort's own game boat brings in fresh fish for dinner, and fruit can be picked outside your bungalow door. The island has a landing strip, with several 50-minute flights weekly from Cairns. Rates: About $130 a day per person, including all meals.

For more information: Queensland Tourist and Travel Corp., 3550 Wilshire Blvd., Suite 1738, Los Angeles, Calif. 90010, (213) 381-3062.

For information about other private island resorts, contact:

*A travel agent.

*Caribbean Tourism Association, 20 E. 46th St., New York City, N.Y. 10017, (212) 682-0435.

*Tahiti Tourist Board, 4405 Riverside Dr., Suite 204, Burbank, Calif. 91505, (818) 841-8802.

*Fiji Visitors Bureau, 3701 Wilshire Blvd., Suite 316, Los Angeles, Calif. 90010, (800) 621-9604.

*Australia Tourist Commission, 636 5th Ave., Suite 467, New York, N.Y. 10111, (212) 489-7550.