When Brett Smith rented a condo at Axis Brickell last year, there were still sweet deals to be found, but when the lease came up for renewal last month, he got a sour note: The rent was spiking 15 percent.

The three-bedroom, three-bath condo would cost $3,800 a month, up from $3,300.

“We actually looked around at other places, and most looked to be around the same price range,” said Smith, a 25-year-old construction project manager who shares the apartment with two friends. “We decided with the cost of moving, we would just stay.”

Smith, who loves the urban lifestyle — “It’s great, and it’s getting better,” he says — has lots of company.

In greater downtown Miami and Brickell, residential rental rates per square foot jumped 10 percent in the first nine months of 2012 from a year earlier, according to a study conducted for Miami Downtown Development Authority by Coral Gables-based Focus Real Estate Advisors.

Rents for the sizzling Brickell neighborhood leaped even more sharply. The average monthly rental rate for Brickell jumped 17 percent to $2,242 in the first nine months of 2012 from the same period in 2010, while the rent per square foot spiked 28 percent over that period, according to additional data from Focus Real Estate Advisors and MLxchange.

Fueling the price increases: Strong demand for rental units and the growing popularity of the downtown and Brickell areas as new restaurants and entertainment spots help mold an urban core that is attractive to young professionals and students but also to an increasingly diverse crowd.

“It’s become like a restaurant Mecca in Brickell,” said Denise Sicuso, sales manager for Esslinger-Wooten-Maxwell Realty’s Brickell downtown office, which handles lots of condo rentals and sales in the area.

With Brickell CitiCentre, a massive $1.05-billion mixed-use complex with retail, entertainment, office and residential, going up at 701 South Miami Avenue, “the interest in the neighborhood is only increasing,” Sicuso added. “When we get rental listings, they’re gone within a week.”

More than 95 percent of rental units in the greater downtown Miami area are occupied, according to the Downtown Development Authority study.

Demand for rental units is strong for many reasons: Tough lending standards for mortgages are making it difficult for many people to buy a home. Coming out of the recession and housing meltdown, many people have credit histories that exclude them from becoming buyers. Others simply don’t want to own.

At the same time, a steady influx of foreigners and others relocating to Miami is bolstering rental demand, as is the gradually improving economy that is enabling some young people who had moved back to the nest with their parents to get their own place.

“There is pent-up demand for rentals, not unique to the downtown or Brickell area,” said Craig Werley, president of Focus Real Estate.

Another factor: Many of the professionally managed rental apartment buildings in South Florida were converted into condominiums before the real-estate market crashed.

Professionally managed apartment buildings account for just 10 percent of Miami’s rental market, down from 20 percent in 2000, according to Werley.

While there is a major push by developers and institutional investors to build more multifamily rental units in South Florida (and around the country), the lag time before new rental units would come to market means supply will be tight for some time.