Housing prices are continuing their upward trajectory in many U.S. cities.

They increased in 15 of 20 major metro markets in September, according to new S&P CoreLogic Case-Shiller Index data released Tuesday.

Nationally, prices in September were up 3.9% compared with a year earlier, despite low inventory and high mortgage rates.

“U.S. home prices continued their rally in September 2023,” S&P Dow Jones Indices Managing Director Craig J. Lazzara said in a statement. He noted that prices have increased for eight consecutive months since prices bottomed out in January 2023.

Detroit saw the greatest price gains in September, increasing 6.7% compared with the same month in 2022. The median sales price for a home in Detroit is $90,000, according to Redfin. 

San Diego took the second spot, increasing 6.5%, while New York came in third, increasing 6.3%. The median sales price for a home in San Diego is $914,000 and $764,000 in New York, according to Redfin.

Home prices in 10 cities reached an all-time high in September: Atlanta, Boston, Charlotte, Chicago, Cleveland, Detroit, Miami, New York, Tampa and Washington.

“Although this year’s increase in mortgage rates has surely suppressed the quantity of homes sold, the relative shortgage of inventory for sale has been a solid support for prices,” Lazzara said. “Unless higher rates or exogenous events lead to general economic weakness, the breadth and strength of this month’s report are consistent with an optimistic view of future results.”

The Northeast and Midwest are the nation’s strongest regions for home prices. The West is the weakest.

Just three of the 20 cities saw lower prices in September, all of them on the West coast: Las Vegas (-1.9%), Phoenix (-1.2%) and Portland (-0.7%).