Abstract: A complete flat Lorentz 3-manifold M is a quotient of Minkowski (2+1)- spacetime by a discrete group G of affine isometries acting freely and properly. The study of such discrete groups relates to the deformation theory of hyperbolic structures on a hyperbolic surface S corresponding to M. Properness of G's action relates to lengthening (or shortening) of geodesics on S. Determining criteria for a proper action is, in general, a difficult problem. When S is a three-holed sphere, the sign of the "Margulis invariant" on each boundary components of S determines whether G acts properly or not -- this is a result we have shown with Drumm and Goldman. We will discuss this theorem and how it applies to deformations of hyperbolic structures on S.