SummaryEstimating the conditional quantiles of outcome variables of interest is frequent in many research areas, and quantile regression is foremost among the utilized methods. The coefficients of a quantile regression model depend on the order of the quantile being estimated. For example, the coefficients for the median are generally different from those of the 10th centile. In this article, we describe an approach to modeling the regression coefficients as parametric functions of the order of the quantile. This approach may have advantages in terms of parsimony, efficiency, and may expand the potential of statistical modeling. Goodness-of-fit measures and testing procedures are discussed, and the results of a simulation study are presented. We apply the method to analyze the data that motivated this work. The described method is implemented in the qrcm R package.