Since the solution of reflection tomography is underdetermined, the use of a priori information is essential to compute a model that is satisfactory from a geological point of view. We propose to compute a model that, classically, matches in a least squares sense the observed travel times and that also satisfies some additional uesful constraints on the portions of reflectors illuminated by the rays. The implementation of this method requires the computation of the Jacobian of the impact point of a ray on a reflector with respect to the model. This computation of the Jacobian of the impact point of a ray on a reflector with respect to the model. This computation is performed by the adjoint state technique, which efficiently produces exact derivatives. The utility of this approach is illustrated on a field data set acquired on fault structures. The method produces a model that matches the kinematic information under the constraint that certain reflectors do not cross the fault. ¿ American Geophysical Union 1995