Americans paid more to rent homes last month, but broader measures suggest that the surging increases of prior years have moderated in much of the country.

Real estate data firm Zillow says the median U.S. monthly rent rose a seasonally adjusted 2.6 percent in March from a year ago to $1,389. That was slightly more than the year-over-year increase of 2.5 percent in February.

Prices ticked up slightly last month in the Los Angeles, Boston, Phoenix and Portland, Oregon, metro areas. Rents fell in Cleveland, Memphis and Oklahoma City.

After sharp increases in 2014 and much of last year, rents cooled between August and February as stepped-up construction put more apartments on the market. For all of 2015, finished construction of multifamily buildings soared 21percent, according to the Commerce Department.