Sales of new U.S. homes fell a steep 12.8% in July as higher prices and limited inventory sidelined would-be buyers.

The Commerce Department said Friday that new homes sold at a seasonally adjusted annual rate of 635,000 units. That’s down from a sharply revised upward rate of 728,000 in June. So far this year, sales have risen just 4.1%.

A shortage of available homes, worsened by a construction slowdown, has pushed up prices and made purchases less affordable for Americans. Land and labor shortages continue to slow down builders, prolonging the housing shortage.

As a consequence, even lower borrowing costs have so far failed to meaningfully boost sales. Mortgage buyer Freddie Mac said Thursday that the average rate on a 30-year loan declined to 3.55% this week, a sharp contrast to a 4.51% rate a year earlier. However, as rising prices outpace wage growth, the effect of historically-low mortgage rates appears to be more limited.

A big 50% jump in sales in the Northeast was offset by declines in the West, Midwest and South.

The median sales price fell to $312,800. That is down 4.5% from a year ago, but marks the highest level since April.

Still, the housing market has shown promising signs since its slowdown last year.

The revisions to the June figure marked the highest annual sales rate since 2007, suggesting that lower mortgage rates may have spurred some buyers. Meanwhile, sales of existing homes— which represent the bulk of the market — rebounded in July. They increased 2.5% after 16 consecutive months of decline.