Most of the million-dollar rentals are unofficial listings, which means they don't show up on the Internet or on broker databases. Brokers generally offer the properties only by word-of-mouth to super-rich prospects.
Yet realtors say at least two properties have already rented for at or close to $1 million for the summer and several others are in active discussions.
Lenz and others say the surge in Hamptons rentals is being driven by hedge funders, the stock market and the super-rich from Russia, Germany, Italy and other countries.
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Pat Petrillo of Sotheby's International Realty in Southampton said the people who rent their homes for $1 million or more are generally "very wealthy themselves," but plan on spending part of the summer in Europe or elsewhere.
"They say, 'Look if someone will pay $1 million for the summer, we'll consider it,'" she said. "They'd be crazy not to."
And who are the renters? No one will name names. But brokers said the renter of one million-dollar rental in Southampton is a wealthy Russian who has rented in the Hamptons before. Another renter in talks for another million-dollar rental is "in finance," according to one broker.
What do you get for your $1 million summer?
Try a property in Water Mill that's renting for around a million for the summer that includes a 14,000-square-foot main house, with eight bedrooms, 10 baths and a home theater. It also has a tennis court, pool and a large guest house.
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An estate in Southampton that recently rented for close to $1 million has an 18,000-square-foot house with 12 bedrooms and 12 baths along with a sprawling guest house and pool house. A tennis court and heated pool are on the 10-acre property. For those who like to do their swimming indoors, the estate has a massive indoor swimming pool with waterfalls and a water slide.
Of course, some million-dollar rentals will never find actual renters. Harald Grant of Sotheby's International Southampton said that "there are really only a few properties that can command that price and the rest are just hoping."
He added that while the Hamptons rental market was on fire in the early spring, it's since cooled a bit after prospective renters decided to buy instead.
"There are a surprising number of properties still available," he said. "Even some oceanfront properties are still available. For a price of course."