(Bloomberg News) The U.S. Supreme Court rejected a challenge to New York City's decades-old rent-stabilization system, leaving intact rules capping prices on almost a million units in one of the country's most expensive cities.

The justices today turned away an appeal by James and Jeanne Harmon, who said the city was violating their constitutional rights by limiting rents on three one-bedroom apartments in their Upper West Side brownstone. The units rent for about $1,000 a month, less than half the price of three similar, unregulated units in the building, the Harmons say.

The couple targeted a 43-year-old state statute that has become part of the city's fabric, shaping its neighborhoods along with the wallets and lifestyles of millions of city residents.

"To the extent that the court is saying rent regulation must stand, I think that's good news for the state of New York," Governor Andrew Cuomo, a Democrat, said at a Manhattan news conference today. "Rent regulations are very important to the tenants of New York."

James Harmon, 68, said in an e-mailed statement after the court action that the U.S. Constitution "does not allow the government to force us to take strangers into our home at our expense for life."

'Dickensian Conditions'

Rent-stabilized apartments have become the stuff of lore and scandal in New York. Former Mayor Ed Koch lived in one for years. So have celebrities including Cyndi Lauper and Carly Simon, according to the New York Times. U.S. Representative Charles Rangel, a Democrat and the former chairman of the tax- writing House Ways and Means Committee, was fined $23,000 last month for using a rent-stabilized apartment in Harlem as a campaign office.

Supporters say the rent-stabilization law protects tenants from prices that otherwise would be out of reach for many New Yorkers.

The median household income for those in the 970,000 rent- stabilized households last year was $37,000, according to the city's most recent housing and vacancy survey, released in February. Four percent of households in rent-stabilized units had incomes of $150,000 or more in 2010, according to the U.S. Census Bureau.

"We would have Dickensian conditions," said Allison Tupper, 72, a retired school teacher. She pays $2,233 a month for a four-room, first-floor apartment with access to a small garden on West 46th Street in Manhattan, in the once rough-and- tumble neighborhood known as Hell's Kitchen that's now rapidly gentrifying. "People would be living in the streets."