Rents rose at a slower pace across the U.S. in June with prices for one-bedroom apartments cooling fastest, according to a new report. 

One-bedroom apartment prices are flat over last month at $1,504, but the increase of 5.8 percent year-over-year marks the softest price gain in nearly two years, data from the online rental platform Zumper showed. 

Rents for two-bedroom apartments increased by just 0.3 percent from last month, while prices fell in 46 of the 100 cities Zumper analyzed. 

Housing costs are cooling due largely to an influx of new construction, including multi-family buildings, hitting the market. Census Bureau figures released earlier this month showed that housing starts increased to an annual rate of 1.63 million units last month, up from 1.34 million in April. 

Starts for buildings with five or more units hit their highest level in nearly four decades at 634,000 in May. 

Yet even as data is showing signs that rents are cooling after more than a year of growth, there are still cities where rents are climbing. 

“This deceleration is, generally, good news for renters, but it does come with caveats,” Zumper CEO Anthemos Georgiades said in a press release. 

“Many cities are still stabilizing after long periods of sharp increases during the pandemic’s Great Migration, and though rents are softening they’re still at record highs in many markets.” 

Zumper data revealed that rents are soaring in New York City, with median monthly prices for a one-bedroom rental reaching $3,900. In Manhattan, median priced one-bedroom apartments are going for $4,000 each month. 

And in Jersey City, N.J., rents hit $3,370. 

Meanwhile, rents rose the most over last month in Memphis, Tenn., surging by more than 6 percent. A median one-bedroom rental there now costs around $1,000 per month.  

The cost of a one-bedroom apartment fell by the most this month in Des Moines, Iowa, where renters can find a median priced rental for $870 monthly.