Zulema Mejias and Oscar Peñas first lived together in Ms. Mejias’s rent-stabilized one-bedroom near her alma mater, Pratt Institute, in Clinton Hill, Brooklyn.

She had moved there in 1999, a few years after immigrating from Cuba, and met Mr. Peñas at a dinner party in Morningside Heights, in Upper Manhattan, thrown by a mutual friend from Spain. Mr. Peñas, 51, a jazz guitarist, instructor and composer who is also from Spain, had studied music in Boston and was living with a roommate in Crown Heights, Brooklyn.

“Oscar arrived late because he got lost in the subway,” Ms. Mejias said. “He sat next to me, and we started talking. I am very talkative. We had so much fun.”

The couple, who married in 2008, still speak Spanish with each other. “When people see us on the street, they think we are tourists,” said Ms. Mejias, 61, who is now her husband’s manager.

They later moved to a Harlem co-op, but were driven out by intolerable noise. The apartment, which they had gut renovated, sold quickly, so they bought a tiny duplex studio condominium in South Slope as an interim measure, glad to return to Brooklyn.

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At first, with a budget of $1.4 million, the couple thought they could buy a bigger condominium. They wanted a music studio for him, an office for her, a guest room for visiting relatives from Barcelona and a spot for sitting outside.

“We used a few real estate agents and changed our minds a few times during the process,” Mr. Peñas said. “We have the taste of Design Within Reach but can afford Ikea, so that’s an issue.”

They wondered whether they were being clear about their wishes. “It is very frustrating when the agents send you listings that are completely opposite to what you are telling them,” Ms. Mejias said. “They would say, ‘You have a very small budget, you are a freelancer, and the only place for you is Ocean Hill.’ It’s the edge of Brooklyn, very far away, and I need to be close to the city. I can’t be that far.”

The couple yearned for a small house in a tranquil residential neighborhood. They contacted Elisa Seeger, an associate broker at The Agency, who acknowledged that the condominiums in their budget often had small bedrooms, little outdoor space, awkward layouts or high monthly charges. But a few possibilities for houses did exist, and a house would have comparatively low taxes.

Among their options:

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