The asynchronous regional regression model (ARRM) is a flexible and computationally efficient statistical model that can downscale station-based or gridded daily values of any variable that can be transformed into an approximately symmetric distribution and for which a large-scale predictor exists. This technique was developed to bridge the gap between large-scale outputs from atmosphere–ocean general circulation models (AOGCMs) and the fine-scale output required for local and regional climate impact assessments. ARRM uses piecewise regression to quantify the relationship between observed and modelled quantiles and then downscale future projections. Here, we evaluate the performance of three successive versions of the model in downscaling daily minimum and maximum temperature and precipitation for 20 stations in North America from diverse climate zones. Using cross-validation to maximize the independent comparison period, historical downscaled simulations are evaluated relative to observations in terms of three different quantities: the probability distributions, giving a visual image of the skill of each model; root-mean-square errors; and bias in nine quantiles that represent both means and extremes. Successive versions of the model show improved accuracy in simulating extremes, where AOGCMs are often most biased and which are frequently the focus of impact studies. Overall, the quantile regression-based technique is shown to be efficient, robust, and highly generalizable across multiple variables, regions, and climate model inputs.