  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.
