Conditions continue to improve for homebuyers in many of the largest U.S. cities, according to recent data from S&P CoreLogic’s Case-Shiller National Home Price Index and Redfin.

The latest reading of the closely watched Case-Shiller index found home price growth unchanged in October compared to the previous month, up 5.5 percent from a year earlier. Among its 10-city index, price growth was more modest at 4.7 percent against last year’s levels, down from 4.9 percent annual growth in September. The 20-city index also grew slower in October.

For the last three months in a row, the Case-Shiller price index has reported slower year-over-year price growth overall. This is true even in cities that have regularly topped its list of biggest gainers. For the fifth consecutive month, Las Vegas saw the fastest rate of year-over-year home price growth of any major city in October (12.8 percent). However, this was down from the previous month’s gain of 13.5 percent. San Francisco, another consistent winner on price growth, saw deceleration in October as well.

David Blitzer, managing director of S&P Down Jones Indices, noted in the newest Case-Shiller report that U.S. home prices were still around 40 percent higher (after adjusting for inflation) than they were around 2012, when the market bottomed out.

Still, more hallmarks of a buyer’s market are creeping into other reports. In a Dec. 12 media release, Redfin said its listing agents faced fewer multiple offer situations (or “bidding wars”) in November compared to a year ago. With 32 percent of Redfin listings receiving more than one competing offer, this was the lowest rate of bidding competition since the company began tracking this data eight years ago. Redfin attributes this to a cooling market, although many of its major markets like Oakland, California, Washington, D.C., and Orange County, California, were still seeing high rates of competition.