Of two yalis open for viewing, one was newly constructed at Kanlica, a small bay on the Asian side. Rebuilt from the original plans, it bears a grand name, the Sipahiler Agasi Mehmet Emin Aga Yalisi, but its size (750 square meters, or about 8,100 square feet, and eight bedrooms) and position puts it on the less extravagant end of the yali scale; for comparison, the mansion bought by the Emir of Qatar has a palatial 94 rooms.

For what it lacks in original structure and character — some yalis are said to be haunted, others laden with legend — a newly rebuilt yali has the advantage of modern kitchens and bathrooms and even, as this one does, an elevator. Renovations and modernization in the older buildings are restricted because of their protected status and construction regulations on the Bosporus.

“We advise that they work with an architect who knows the Bosporus,” Mr. Ozcan says of prospective buyers.

Another property open for viewing is the Ethem Pertev Bey Yali, which has a distinctive carved veranda and is one of the few historical yalis available for rent. Built in the 1860s for Fatma, a princess said to be a favorite of Sultan Abdulmecid I, the yali is named for a subsequent owner, a pharmacist who created a famous skin cream.

The main house, and a second wing built around 1900, are modernized but furnished with Ottoman touches, including a portrait of an Ottoman courtier in a swooping, balloon-shaped turban, a grandfather of the current owner. A modern guest wing at the back makes the house 500 square meters, with a total of seven bedrooms and bathrooms.