The country's median national rent for single-family detached homes climbed to $2,395, a big 19.75% leap from the same period two years ago and a 6% rise from that time frame last year, according to a new report by HouseCanary. 

But while rents are rising, by the end of the first quarter rental properties were staying on the market for an average of 30.4 days, roughly a 43.4% increase since the same period last year and a 12.6% increase since the last quarter of last year.

Some of the markets where days on the market are increasing are in the Southeast, in some cases noticeably. In New Orleans-Metairie, La., the change represented 175%; Raleigh, N.C., was 167% higher and Durham-Chapel Hill, N.C., was at 140%. The lowest on the list was Riverside-San Bernardino-Ontario, Calif., where the increase was still high but a much lower 89%.