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We present an updated analysis of the gamma-ray flux from the directions of classical dwarf spheroidal galaxies, deriving new constraints on WIMP dark matter (DM) annihilation using a decade of Fermi-LAT data. Among the major novelties, we infer the dwarfs' J-factors by including new observations without imposing any a priori parametric profile for the DM distribution. While statistically compatible with results obtained from more conventional parameterisations, this procedure reduces the theoretical bias imposed on the data. Furthermore, we retain the full data-driven shape of the J-factors' empirical probability distributions when setting limits on DM, without imposing log-normality as is typically done. In conjunction with the data-driven J-factors, we use a new method for estimating the probability distribution function of the astrophysical background at the dwarf position, fully profiling over background uncertainties. We show that, for most classical dwarfs, the background systematic uncertainty dominates over the uncertainty on their J-factors. Raw distributions of J- and D-factors (the latter being the analogous of J-factors for decaying DM) are available upon request.