We descibe the use of reflected PP, SS, and converted PS/SP phases in a joint inversion to determine P-and S-wave velocity-depth functions. For an adequate determination of Poisson's ratio, the P- and S-wave velocity functions must be coupled in the inversion scheme. This coupling can be attained in different ways. In this article, we use the PS/SP converted phases to achieve it. In order to model gradient zones and to prevent any bias due to our choice of parameterization, our models consist of a large number of constantvelocity thin layers. The solution of the inversion problem estimates the thicknesses of these layers. The number of unknowns (layer thicknesses) is greater than the number of data points and the one-dimensional inverse problem is an underdetermined system of equations. A weighted damped least-squares inversion algorithm using the (τ, p) formulation is used. The input data for this inverse problem consist of intercept-time ray-parameter pairs picked from (τ, p) slantstacked wide-angle seismic reflection source gathers. When this procedure is used to invert only a single type of reflected waves, then the solution is strongly biased by the assignment of the data picks, (τ, p) paris, to a particular layer. By using the (τ, p) picks for the reflected PP, the reflected SS, and the converted PS/SP in a single joint inversion, the algorithm becomes more robust. Furthermore, the resolution of the P and S velocity-depth functions is greatly increased. The resolution kernels become sharper, decreasing the width of the main lobe by 10 to 50% and increasing their height by 20 to 40%. This increase in resolution in the velocity-depth functions can produce a decrease of approximately 50% in the error estimates of Poisson's ratio profiles.