  In order to place limits on dark matter (DM) properties using $\gamma$-ray
observations, previous analyses have often assumed a very simple
parametrisation of the $\gamma$-ray annihilation yield; typically, it has been
assumed that annihilation proceeds through a single channel only. In realistic
DM models, annihilation may occur into many different final states, making this
quite a rough ansatz. With additional processes like virtual internal
bremsstrahlung and final state radiation, this ansatz becomes even more
incorrect, and the need for scans of explicit model parameter spaces becomes
clear. Here we present scans of the parameter space of the Constrained Minimal
Supersymmetric Standard Model (CMSSM), considering $\gamma$-ray spectra from
three dwarf galaxies, the Galactic Centre region and the broader Galactic halo,
as obtained with the High-Energy Stereoscopic System (H.E.S.S.). We present a
series of likelihood scans combining the H.E.S.S. data with other experimental
results. We show that observations of the Sagittarius, Carina and Sculptor
dwarf galaxies disfavour the coannihilation region of the CMSSM and models with
large annihilation cross-sections. This is true even under reasonable
assumptions about the DM density profiles, and constitutes the strongest
constraint to date on coannihilation models within the CMSSM. The Galactic halo
has a similar, but weaker, effect. The Galactic Centre search is complicated by
a strong (unknown) $\gamma$-ray source, and we see no effect on the CMSSM
parameter space when assuming a realistic Galactic Centre DM density profile.
