Much of our knowledge about future changes in precipitation relies on global (GCMs) and/or regional climate models (RCMs) that have resolutions which are much coarser than typical spatial scales of precipitation, particularly extremes. The major problems with these projections are both climate model biases and the gap between gridbox and point scale. Wong et al. (2014) developed a model to jointly bias correct and downscale precipitation at daily scales. This approach, however, relied on pairwise correspondence between predictor and predictand for calibration, and, thus, on nudged simulations which are rarely available. Here we present an extension of this approach that separates the downscaling from the bias correction and in principle is applicable to free-running GCMs/RCMs. In a first step, we bias correct RCM-simulated precipitation against gridded observations at the same scale using a parametric quantile mapping (QMgrid) approach. In a second step, we bridge the scale gap: we predict local variance employing a regression-based model with coarse-scale precipitation as a predictor. The regression model is calibrated between gridded and point-scale (station) observations. For this concept we present one specific implementation, although the optimal model may differ for each studied location. To correct the whole distribution including extreme tails we apply a mixture distribution of a gamma distribution for the precipitation mass and a generalized Pareto distribution for the extreme tail in the first step. For the second step a vector generalized linear gamma model is employed. For evaluation we adopt the perfect predictor experimental setup of VALUE. We also compare our method to the classical QM as it is usually applied, i.e., between RCM and point scale (QMpoint). Precipitation is in most cases improved by (parts of) our method across different European climates. The method generally performs better in summer than in winter and in winter best in the Mediterranean region, with a mild winter climate, and worst for continental winter climate in Mid- and eastern Europe or Scandinavia. While QMpoint performs similarly (better for continental winter) to our combined method in reducing the bias and representing heavy precipitation, it is not capable of correctly modeling point-scale spatial dependence of summer precipitation. A strength of this two-step method is that the best combination of bias correction and downscaling methods can be selected. This implies that the concept can be extended to a wide range of method combinations.