U.S. home prices rose at a faster pace in December as mortgage rates remained low and a falling supply of available properties set off bidding wars between buyers.

The S&P CoreLogic Case-Shiller 20-city home price index climbed 2.9% in December from a year earlier after posting a 2.5% gain in November.

Prices rose in all 20 cities, led by increases of 6.5% in Phoenix, 5.3% in Charlotte, North Carolina and 5.2% in Tampa, Florida. Prices rose just 1% in Chicago and New York.

Just 1.42 million homes were on the market at the end of January, down nearly 11% from a year earlier. The limited supply pushes prices higher. The rate for a benchmark 30-year, benchmark mortgage loan was 3.49% last week, down from 4.35% a year earlier.

Prices in the 20 cities are up 63% from the low they reached in March 2012 in the wake of the financial crisis and 6% above their July 2006 pre-crisis peak.