They probably belonged to the former resident of her $800 Murphy bed-equipped studio apartment on Northwest 22nd Avenue and Glisan Street—the person who painted the walls bright yellow and left the kitchen and bathroom coated in so much grime they took hours to clean.

But Bozanich, 29, was thrilled. Not with the filth, of course, but with the fact that after several weeks of searching, she had finally found an apartment.

When her short-term lease ran out, it took even longer to find another place—she and her future roommates spent two months looking. They finally found a house in the Concordia neighborhood that, on their initial visit, contained seven aquariums of assorted reptiles. They grabbed it. (The reptiles later moved out.)

“I couldn’t believe how fortunate we were,” Bozanich says, noting that friends have looked even longer without finding a place that fit their budget. “We really counted our blessings on this one.” 

Portland has long had a reputation as an affordable West Coast city, boasting rents that are lower on average than in Seattle or San Francisco. 

But affordability only matters to people who can actually find an apartment.

The Portland area has the tightest rental market of any major city in the United States, according to the U.S. Census Bureau. Only 3 percent of apartments here are vacant at any given time—half as many as were available three years ago.

The days of apartment companies offering a month off or free parking are long gone. Apartment managers and landlords see people lined up outside rentals, many with applications and blank checks in hand. Desperate renters are finding places have been rented within minutes after being posted on Craigslist. Some renters have offered to pay above the advertised rent if it means they can land the place.

“We’ll put something up and hear within five minutes they’ve heard about a property and want to have a viewing,” says Bette Durham, a broker at Mainlander Property Management. “Unfortunately, we can’t pull extra properties out of our hats.” 

The fierce demand for apartments in short supply is causing Portland’s reputation for affordability to slip away.

Rents have risen 17 percent in the last five years in the Portland metro area, according to the Metro Multifamily Housing Association, a trade group of landlords and rental managers. That’s well above the national average of 12 percent during that same time.

No Rooms to Spare: The 25 Major US Cities with the Lowest Vacancy Rate:

View No Rooms to Spare in a full screen map. Source: The U.S. Census Bureau measures vacancy rates in 75 markets nationwide. These are the 25 lowest rates of cities that have at least 500,000 people.

And rents have jumped 8 percent this year—more than three times faster than the nationwide rate.

Rents are climbing even faster in downtown and the Pearl District, where they’ve jumped 16 percent this year, according to the records.

As a result, many people are being pushed to the edges of the city, adding to the hidden costs of housing, including more money and time spent commuting to jobs.

“If we care about people having choices about where they live, if we don’t want to concentrate poverty on the edges of our city, then we need a range of housing choices in each neighborhood,” says City Commissioner Nick Fish, who oversees the Housing Bureau. “We’re limiting people’s choices about where they can live and raise a family.”

In a market where demand is so high, developers should be lining up to build more rental properties. But many say they face a dilemma. High-end projects still can’t charge the rents they need to make them pencil out. And more modest building projects, where the rents are lower, are having trouble getting financing.

That might also be true in other cities. But in Portland, even during the building boom in the last decade, few developers had any interest in apartments—they built condos instead. That left the city short on rentals as the demand grew—from people who cannot afford to buy a house, those who had to give up the houses they owned, and a steady stream of newcomers who moved here despite the recession.

Mark McMullen, the interim state economist, says the influx was mostly young people willing to move here without jobs.

“Portland is still a magnet,” he says. “And that’s a good thing.”

Except if you can’t find an affordable place to live—in some cases, any place to live.