NEW YORK — The stairs in the 155-year-old West Village apartment house tilt, and you could probably do an archaeological investigation on the layers of paint in the entryway. And the little one-bedroom shared by Miranda Dempster and her partner, Gus McKay, in this beat-up building is a rental, which is always a design challenge. How much money would anyone be prepared to sink into it?

And yet, with a renovation that cost no more than $3,000 and midcentury thrift-shop treasures she brought over from her native New Zealand, Dempster, a 41-year-old freelance art director, converted a dreary, cramped tenement into a bright, upbeat home.

One key cost saver: She did the kitchen herself, replacing a full-size refrigerator with a half-size one topped by a butcher block to increase counter space, and replacing the battered kitchen cabinets with shelves.

“When I moved in, the kitchen was totally disgusting, with brown fake-veneer cabinets and a Formica bench” — that means counter — “with the Formica all peeling off,” says Dempster, who has lived here for 12 years.

“It was very gross. One Thanksgiving I had a few days off and I thought, ‘I’m just going to do it.’ I got the guy at Home Depot to explain the different edges of tiles, and I figured it out pretty quickly. I tore out the cabinets and put in Ikea shelves.

“I got the butcher block at the Bowery Kitchen Supply store in Chelsea Market. I don’t think the whole kitchen cost more than $1,000. Then I had a friend come in and re-sand the floors and paint. That cost me about $2,000.”

Dempster gestures at the windows overlooking Abingdon Square, a little triangular park across the street.

“One of the things I love is the light,” she says. “It’s really great at night with no buildings obstructing it. In the winter, when there are no leaves and it’s easier to see, I would just sit here and gaze out.”

Park views, even in scruffy buildings, do not come cheap in Manhattan.

Dempster and McKay, a 45-year-old tailor for the fashion label Tocca and fellow New Zealander who moved in a year ago, pay $2,300 a month for their apartment, which they estimate to be no larger than 600 square feet. And with two people in a small space, they must furnish very carefully.

All the furnishings belong to Dempster. Some date back to her college years in New Zealand. There’s a metal weave chair she found for $30, which she believes is a copy of a Harry Bertoia piece, and another chair by the Dutch designer Bob Roukema, who settled in New Zealand, that Dempster found in a secondhand store for $15 and realized was a sought-after collectible.

She also has a two-tier kidney-shaped glass side table (designer unknown) that she bought from a friend in New Zealand for $150, and a fake Saarinen table and four chairs, for which she paid $300 at the 26th Street flea market in Manhattan 10 years ago.

The most expensive item is a Jens Risom sofa, which she bought for $1,000.

The contributions of McKay, who joins the conversation late after coming home from work, have of necessity been minor. “I was told expressly to bring only things I really needed,” he says.

He gestures around the room. “The ubiquitous New Zealand seafood poster that you see everywhere is mine,” he says, dryly. “That painting is mine. I cook; the knives in the kitchen are mine. That jacket that I walked in with is mine.”