  We compute the expected dimension of the moduli space of torsion-free rank 2
sheaves at a point corresponding to a stable reflexive sheaf and give
conditions for the existence of a perfect tangent-obstruction complex on a
class of smooth projective threefolds; this class includes Fano and Calabi-Yau
threefolds. We also explore both local and global relationships between moduli
spaces of reflexive rank 2 sheaves and the Hilbert scheme of curves.
