In model-based coding of facial images, the accuracy of motion and depth parameter estimates strongly affects the coding efficiency. MBASIC is a simple and effective iterative algorithm (recently proposed by Aizawa et al.) for 3-D motion and depth estimation when the initial depth estimates are relatively accurate. In this correspondence, we analyze its performance in the presence of errors in the initial depth estimates and propose a modification to MBASIC algorithm that significantly improves its robustness to random errors with only a small increase in the computational load.