  We propose various ways of adding mass terms to three-dimensional twistor
string theory. We begin with a review of mini-twistor space--the reduction of
D=4 twistor space to D=3. We adapt the two proposals for twistor string theory,
Witten's and Berkovits's, to D=3 super Yang-Mills theory. In Berkovits's model,
we identify the enhanced R-symmetry. We then construct B-model topological
string theories that, we propose, correspond to D=3 Yang-Mills theory with
massive spinors and massive and massless scalars in the adjoint representation
of the gauge group. We also analyze the counterparts of these constructions in
Berkovits's model. Some of our constructions can be lifted to D=4, where
infinitesimal mass terms correspond to VEVs of certain superconformal gravity
fields.
