This paper presents a new optimization approach for estimating vocal tract configurations from the speech signal. The scheme concatenates a gradient search and linear successive approximation that provides fast convergence and small errors. The objective function is generated by the least-absolute-value (11 -norm) error between the model-derived and the speechderived first three formants. The gradient search is accelerated by using an algorithm inspired by the Fletcher -Reeves method. Linear successive approximation assures convergence in the region near the optimum articulatory vector. Constraints are imposed on the articulatory parameters to avoid physiologically impossible configurations.