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Dynamical downscaling (DD) consists in using archives of Coupled Global Climate Models (CGCM) simulations as the atmospheric and sea-surface boundary conditions (BC) to drive nested, Regional Climate Model (RCM) simulations. Biases in the CGCM-generated driving BC, however, can have detrimental impacts on RCM performance. It is well documented for the historical period that CGCM-simulated sea-surface temperatures (SST) suffer substantial biases, especially important near coastal regions. Assuming that these SST biases are time-invariant, they could in principle be subtracted from century-long CGCM projections before being used to drive RCMs. This paper investigates the performance of a 3-step DD approach as follows. The CGCM-simulated sea-surface temperatures (SST) are first empirically corrected by subtracting their systematic biases; the corrected SST are then used as ocean surface BC for an atmosphere-only GCM (AGCM) simulation; finally this AGCM simulation provides the atmospheric lateral BC to drive an RCM simulation. This is what we refer to as the 3-step approach CGCM-AGCM-RCM of DD, which can be compared to the traditional 2-step approach CGCM-RCM consisting of driving an RCM simulation directly by CGCM-generated BC. In this paper we compare the results obtained with the two approaches, for present and future climates under RCP8.5, using the fifth-generation Canadian Regional Climate Model (CRCM5) with a grid mesh of 0.22 degrees over the North American CORDEX domain, driven by two CMIP5 models: the Canadian Earth System Model of the Canadian Centre for Climate modelling and analysis (CanESM2) and the Earth System Model of the Max-Planck-Institut fur Meteorologie (MPI-ESM-MR). The results show that, in current climate, the seasonal-mean 2-m temperature fields simulated with the 3-step DD have generally smaller biases with respect to the observations than those simulated with the 2-step DD; in fact the performance of the 3-step DD simulations often approaches that of the reanalyses-driven simulation. For the seasonal-mean precipitation field, however, the differences between the two DD methods are not conclusive. Differences between the projected climate changes with the two DD methods vary substantially depending upon thevariable being considered. Differences are particularly important for temperature: over the bulk of the North American continent, the 3-step DD projects more warming in winter and less in summer. This result highlights the nonlinearities of the climate system, and constitutes an additional measure of uncertainty with DD.