The vast majority of states, as well as many local agencies, now use statistical end-result specifications to encourage high-quality construction by awarding payment in proportion to the level of quality received. Because many of the specification procedures were developed by intuition and guesswork, more recent efforts have been directed at converting the specifications to true performance-related specifications, thus providing a rational and defensible basis for price-adjustment decisions. To develop practical and effective specifications of this type, it is necessary to have at least approximate quantitative (mathematical) models of the manner in which construction quality affects performance. By using pavement smoothness as an example, a method is presented by which empirical performance data can be combined with logical assumptions about mathematical form and boundary conditions to develop quantitative models sufficiently accurate for use with statistical construction specifications.