Dwarf galaxies represent a powerful probe of annihilating dark matter particle models, with gamma-ray data setting some of the best bounds available. A major issue in improving over existing constraints consists in the limited knowledge of the astrophysical background (mostly diffuse photons, but also unresolved sources). Perhaps more worrisome, several approaches in the literature suffer of the difficulty of assessing the systematic error due to background mis-modelling. Here we propose a data-driven method to estimate the background at the dwarf position and its uncertainty, relying on an appropriate use of the whole-sky data, via an optimisation procedure of the interpolation weights. While this article is mostly methodologically oriented, we also report the bounds based on latest Fermi-LAT data and updated information for J-factors for both isolated and stacked dwarfs. Our results are very competitive with the Fermi-LAT ones, while being derived with a more general and flexible method. We discuss the impact of profiling over the J-factor as well as over the background probability distribution function, with the latter resulting for instance crucial in drawing conclusions of compatibility with DM interpretations of the so-called Galactic Centre Excess.
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