This two-bedroom, one-bath cottage in Amagansett is set on a 0.6-acre lot and has been in the same family for three generations. The asking price is $2.75 million.

The current owner inherited the property from her late father, who used the home year-round and added insulation and propane gas heat, says broker Htun Han, principal broker for the Hamptons Realty Group. The listing agent is Victoria Handy Smudzinski.

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“They live on the West Coast — to bring her and her family over to enjoy the house is a challenge, if not a practical impossibility to do on a regular basis,” Han says, who adds that the home has been a year-round rental in recent years.

A stone path through a grassy front lawn leads to a screened-in front porch, which opens to the home’s living room and dining area. There is a small kitchen, two bedrooms and a full bath.