That’s what two engineers set out to do some 18 months ago. The result is Tuft and Needle, a startup that began selling foam mattresses mostly through a slick website at the end of 2012. The company remains tiny, having passed the $1 million sales mark after one year in an industry that by some estimates generates $7 billion in revenue annually.

But in its short life, Tuft and Needle has earned something to brag about. Though its mattresses, at $400 for a queen-sized model, are relatively inexpensive, customers seem to love them. The young company began selling through Amazon in the fall, and its mattresses soon reached No. 1, when rated by customer reviews. Its products have earned 154 five-star and 16 four-star ratings. In the only negative review, a customer gave it a single star complaining that the mattress was too firm for his taste.

“It’s pretty cool to see this tiny team become the No. 1-rated mattress team on Amazon,” says Caleb Elston, the co-founder and CEO of Delighted, a startup that helps businesses collect customer feedback and that counts Tuft and Needle among its customers.

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Tuft and Needle was co-founded by John-Thomas Marino, 28, and Daehee Park, 25. The two were college buddies at Penn State a few years earlier, where both dabbled in the startup world. After reuniting briefly at a Silicon Valley firm, they left in mid-2012 to launch their own company. “We wanted to take everything we learned tech-wise, in software and business processes, and apply it to something old-fashioned,” says Marino, who goes by JT. They picked mattresses after Marino went through what he describes as a significant amount of pain to buy a $3,200 memory foam mattress. “It was a terrible experience,” he says.

The two set out to research what it would cost to make mattresses. It was not easy going: Several manufacturers wouldn’t even talk to them. What they eventually found out is now summarized on their website and reads a bit like a consumer manifesto.

Most mattresses, they say, typically cost only hundreds of dollars to produce. But the markups to cover overhead, distributor fees, and profits are enormous — as much as 1,000%. “More of your dollars go to pay for the sales commissions, advertising costs, and outrageous profits than the actual ingredients of the product,” they write. In contrast, Tuft and Needle offers “an honestly crafted mattress at a fair price.”

Tuft and Needle’s claims have attracted some detractors. On a blog post on the website Hacker News, where Marino and Park described their approach, one critic described the company’s product as “very low end” and its marketing claims as “half truths.” Another commenter compared the mattresses to futons.

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Marino says mass-produced futons are far cheaper to make and not really comparable to his company’s foam mattresses. He also says that manufacturers have been making increasingly thick mattresses just so they can charge consumers more. The company’s 5-inch mattresses are more comfortable than most thicker coil or foam mattresses, he says. “Thickness doesn’t matter,” Marino says. “It’s all spin.” (Many consumers seem to agree.) The company will soon release a 10-inch model that he says will silence its critics.

Tuft and Needle’s mattresses are made in the U.S., from three layers of foam, and are covered in a knitted fabric. They are assembled and shipped from a facility in Los Angeles. Marino and Park say they researched the ideal foam combinations and fabrics to come up with their first product. Like a tech company, they have continued iterating on the product, incorporating suggestions made by their customers. “We make changes to the product monthly,” says Marino.

The two also wrote their own fulfillment software to communicate with suppliers, who before that took orders via e-mail. As a result, the number of errors dropped dramatically. And they use analytics to determine the preferences of their customers and customize their website accordingly. The company is self-funded but has recently attracted the attention of investors, Marino says.

“The growth is consistent, and it’s all based on word of mouth,” he adds.

While it is officially based in Phoenix, the company is largely virtual, with its 10-or-so employees, most of them in customer service, who work from remote locations across the country. When they took the top-reviewed slot in the mattress category on Amazon, they celebrated with a glass of champagne. “We all got on a Skype call and tapped our glasses to the screen,” Marino says.