  The next generation of ground-based Imaging Air Cherenkov Telescopes (IACTs)
will play an important role in indirect dark matter searches. In this article,
we consider two particularly promising candidate sources for dark matter
annihilation signals, the nearby dwarf galaxies Draco and Willman 1, and study
the prospects of detecting such a signal for the soon-operating MAGIC II
telescope system as well as for the planned installation of CTA, taking special
care of describing the experimental features that affect the detectional
prospects. For the first time in such a study, we fully take into account the
effect of internal bremsstrahlung, which has recently been shown to
considerably enhance, in some cases, the gamma-ray flux at the high energies
where Atmospheric Cherenkov Telescopes operate, thus leading to significantly
harder annihilation spectra than traditionally considered. While the detection
of the spectral features introduced by internal bremsstrahlung would constitute
a smoking gun signature for dark matter annihilation, we find that for most
models the overall flux still remains at a level that will be challenging to
detect unless one adopts rather (though by no means overly) optimistic
astrophysical assumptions about the distribution of dark matter in the dwarfs.
