  We consider 3-dimensional hyperbolic cone-manifolds, singular along infinite
lines, which are ``convex co-compact'' in a natural sense. We prove an
infinitesimal rigidity statement when the angle around the singular lines is
less than $\pi$: any first-order deformation changes either one of those angles
or the conformal structure at infinity, with marked points corresponding to the
endpoints of the singular lines. Moreover, any small variation of the conformal
structure at infinity and of the singular angles can be achieved by a unique
small deformation of the cone-manifold structure.
