The aim of a data reduction process is to minimize the influence of data acquisition imperfections on the estimation of the desired astronomical quantity. For this purpose, one must perform appropriate manipulations with data and calibration frames. In addition, random-error frames (computed from first principles: expected statistical distribution of photo-electrons, detector gain, readout-noise, etc.), corresponding to the raw-data frames, can also be properly reduced. This parallel treatment of data and errors guarantees the correct propagation of random errors due to the arithmetic manipulations throughout the reduction procedure. However, due to the unavoidable fact that the information collected by detectors is physically sampled, this approach collides with a major problem: errors are correlated when applying image manipulations involving non-integer pixel shifts of data. Since this is actually the case for many common reduction steps (wavelength calibration into a linear scale, image rectification when correcting for geometric distortions,...), we discuss the benefits of considering the data reduction as the full characterization of the raw-data frames, but avoiding, as far as possible, the arithmetic manipulation of that data until the final measure of the image properties with a scientific meaning for the astronomer. For this reason, it is essential that the software tools employed for the analysis of the data perform their work using that characterization. In that sense, the real reduction of the data should be performed during the analysis, and not before, in order to guarantee the proper treatment of errors.