  We study neutralino dark matter within a semi-realistic type I string model,
where supersymmetry breaking arises from F-terms of moduli fields parameterised
in terms of Goldstino angles, which automatically gives rise to non-universal
soft third sfamily and gaugino masses. We study the fine-tuning sensitivities
for dark matter and electroweak symmetry breaking across the parameter space of
the type I string model, and compare the results to a similar analysis in the
non-universal MSSM. Within the type I string model we find that neutralino dark
matter can be naturally implemented in the $\stau$ bulk region, the $Z^0$
resonance region and the maximally tempered Bino/Wino/Higgsino region, in
agreement with the results of the non-universal MSSM analysis. We also find
that in the type I string model the ``well-tempered'' Bino/Wino region is less
fine-tuned than in the MSSM, whereas the $\stau$ co-annihilation region
exhibits a significantly higher degree of fine-tuning than in the MSSM.
