Some of the best-known results in mechanism design depend criticallyon Myerson’s (Math Oper Res 6:58–73, 1981) regularity condition. For example,the second-price auction with reserve price is revenue maximizing only if the typedistribution is regular. This paper offers two main findings. First, a new interpretationof regularity is developed—similar to that of a monotone hazard rate—in terms ofbeing the next to fail. Second, using expanded concepts of concavity, a tight sufficientcondition is obtained for a density to define a regular distribution. New examples ofregular distributions are identified. Applications are discussed.