  Paleo-detectors are a recently proposed method for the direct detection of
Dark Matter (DM). In such detectors, one would search for the persistent damage
features left by DM--nucleus interactions in ancient minerals. Initial
sensitivity projections have shown that paleo-detectors could probe much of the
remaining Weakly Interacting Massive Particle (WIMP) parameter space. In this
paper, we improve upon the cut-and-count approach previously used to estimate
the sensitivity by performing a full spectral analysis of the background- and
DM-induced signal spectra. We consider two scenarios for the systematic errors
on the background spectra: i) systematic errors on the normalization only, and
ii) systematic errors on the shape of the backgrounds. We find that the
projected sensitivity is rather robust to imperfect knowledge of the
backgrounds. Finally, we study how well the parameters of the true WIMP model
could be reconstructed in the hypothetical case of a WIMP discovery.
