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In 2009, Jayna Cooper spotted an unremarkable house on a sliver of land for only $225,000 in the middle of Los Angeles. She jumped to buy it.

Sure, the lot was tiny -- 2,231 square feet -- but Cooper saw an opportunity to flex her creative muscle. Then 27 years old and with a Master of Architecture degree from the University of Southern California, Cooper got to work demolishing the old structure to make room for her vision.

It was the first house she built and owned. Six years later, if all goes well, it will be the first house she sells.

"I really love this house," says Cooper of the boxy ultramodern home she just listed for $685,000.

The 1,761-square-foot house stands 3 stories tall, lending it an advantage in a neighborhood of one- and two-story homes.

"There's nothing blocking any view. You can see the tops of palm trees for miles and miles, in a place where you wouldn't think you'd get such great views," Cooper says.

Building skyward was also practical -- the home cantilevers over the driveway, with the house itself serving as a carport. This design allows space for two vehicles to turn around (a city ordinance Cooper was forced to plan the entire house around). With the first floor used mainly used for storage, there's ample room for living.

The second floor houses the kitchen and living area, while the third floor features the master bedroom. Cooper calls her two-bedroom home "an upside-down townhouse."

She oversaw the entire process, from design to construction. "The goal was to find ordinary, fairly inexpensive construction materials to make interesting architecture."

The exterior is made of plaster and corrugated galvanized metal, supported by reinforced steel beams anchored to an underground block of concrete.

The interior features bamboo flooring and steel cable rails for the stairwell.

Not everything was done with the budget in mind. Cooper splurged on a few designer touches, including the triple-jointed Kohler Karbon kitchen faucet and the light fixtures resembling tadpoles.

Along with the challenge of building up, Cooper had to account for the bustle of a busy street. She planned for the less-trafficked areas of the home (closets, cabinets, and bathrooms) to face the street, creating a cushion against the sound. "When you're inside, you can't hear the traffic at all," she says.

Outside, she installed a sliding gate and privacy fence that's open on the bottom. Passers-by can't see in, but you "always know what's going on outside," Cooper says.

Cooper's ingenuity has paid off. The house has been on the market for less than two weeks and there are already two cash offers, with more expected, according to listing agent Jerry Hsieh. About 70 people attended a recent weekend open house, he says.

"Everybody loves it. They're blown away by the scale and the views and the design of it for that price," Hsieh says. "It's a pretty remarkable price to get a home like that in West L.A."

Plus, the roof seems like a sweet spot to watch the fireworks.