Petit St Vincent is a private islet of just 135 acres in the Grenadines, the southernmost of the Lesser Antilles, an idyllic place of densely forested hills and coral-sand beaches, where the emptiness makes it feel like unclaimed wilderness. From its highest point, Marni Hill, you can see almost the entire Grenadines archipelago: the purple hills of St Vincent in the north; Grenada just about visible to the south. And in between: Mustique, Canouan and the sublimely beautiful Tobago Cays. Yet on the island itself, scarcely a sign of habitation is visible: no vehicles, no other people, barely a building; just jungle giving way to beaches (Caribbean and Atlantic) and the horizon beyond. And no sound but birdsong and the wind in the trees.
There are just 22 one and two-bedroom cottages and villas, so one can be virtually assured of a stretch of beach to oneself. Indeed, if you choose to dine on your veranda, you could spend a week here interacting with no one but the staff.
Former US airman Haze Richardson happened on the islet while sailing in the Grenadines in 1963, bought it, and by the end of that decade was beginning to establish the small hotel. Designed in collaboration with Arne Hasselqvist, the architect responsible for the first villas on Mustique, the cottages owe something to the era in which they were built: simple structures of blue bitch stone found on the island and purpleheart wood, with cane furniture, rush mats and practically no mod cons: no keys, no TVs, no phones, no air-con, no pool, no Wi-Fi, not even mosquito nets (and the insects can be vicious). In many ways, it's like travelling back in time. Not least because this is surely the only hotel in the world that provides a can of spray starch along with an iron, and where the soap is old-fashioned Palmolive.
In 2010, however, the island was sold to Phil Stephenson, a Washington lawyer turned oil magnate, and Robin Paterson, a British-born, Barbados-based property developer, who upgraded the accommodation: lightening the oppressive, brown decor with something paler and more Caribbean, replacing the twin double beds with a single kingsize, adding a new beachside restaurant and a spa - targeted as much at passing yachts as resident guests - and engaging a general manager with an Aman resorts background. Petit St Vincent in its new incarnation was unveiled in 2012.
The sense of the privacy is PSV's compelling selling point. Go from Easter to June, when the foliage is in bloom (and hotel rates tend to be less expensive than the popular winter season). The island exudes a powerful allure, a place where time really does seems to slow, you live by the sun and your cares melt away.
Website: petitstvincent.com
Price: Doubles from US$1,260 (about £845), full board
Parrot Cay, Turks and Caicos
This 1,000-acre private-island hotel is by far the most alluring of the 49 cays that make up Turks & Caicos, a 75-minute flight from both Miami and Nassau followed by a half-hour boat transfer. Hence its reputation as a celebrity magnet - not that it's off-limits to lesser mortals.
Owned by Christina Ong's COMO Hotels & Resorts, Parrot Cay has the look of a New England beach house: lots of white tongue-and-groove panelling and pale upholstery, with tropical accents in the Balinese teak; cane and rattan furniture and wafting mosquito nets. But its real glories are its mostly empty mile-long beach of the palest, softest sand and intensely turquoise water, which deepens, past a line of white breakers, to an inky indigo at the reef. The atmosphere is chilled and understatedly glamorous (though not intimidatingly so), and the predominantly Asian staff have that extraordinary knack of figuring out what you want before you've thought of it. And its lagoon-facing spa, the COMO Shambhala Retreat - the brand that sets the standard to which all spas should aspire - is outstanding.
Website: comohotels.com/parrotcay
Price: Doubles from about US$840 (about £560)