This paper addresses the problem of estimating the 3D rigid pose of an object from its digitized X-ray projection. Certain applications in medical image analysis or non-destructive testing demand an extremely high level of accuracy: early detection of orthopedic prosthesis migration or the detection of defects or occlusion in manufactured objects requires sub-millimeter precision. It is also possible after registration to use subtraction to enhance features absent from the shape model. We considered the cases of homogeneous (CAD models) and inhomogeneous (map obtained from tomodensitometry) X-ray attenuation in an optimization framework based on a mutual information similarity measure(SM). Pose is recovered with submillimeter accuracy and high precision for both screen-film and computed radiographs by three major enhancements of the existing iconic methods: i) special care is given to the model of Parzen distribution used in the mutual information estimator (data pre-sphering in the bivariate case and bandwidth estimation in the univariate case); ii) a quasi-global optimization scheme based on the stochastic clustering is used in conjunction with an object mesh resampling stage to reduce variance of the final pose estimator; iii) nonlinear response of screen-film radiographs is also modeled.