Using a Monte Carlo approach, we determine the mantle viscosity profiles which best fit the currently observed very long baseline interferometry (VLBI) baseline lengths in North America. Our inversion, which is based on the deglaciation model ICE-1 and on the most recent VLBI global solution , demonstrates that the observations are best fit for a shallow upper mantle with viscosity below the traditional reference value of 1021 Pa s. The lower mantle viscosity cannot be unequivocally determined by means of VLBI data alone. In fact, our inversion indicates that two distinct solutions are possible. The first is characterized by a lower mantle with viscosity of a few times 1021 Pa s, a value in agreement with that derived by the global set of relative sea level curves. The second admissible solution corresponds to a lower mantle with viscosity close to 1023 Pa s. We have found that the viscosity of the transition zone may vary between 5¿1021 and 5¿1022 Pa s, i.e., larger than the lowest admissible values found for the lower mantle viscosity. The results of the Monte Carlo inversion are essentially stable with respect to time, since similar viscosity profiles are suggested if the VLBI global solution 1014 is employed, which contained data through July 1995. However, the increased precision of VLBI data since that time has somewhat narrowed the set of admissible viscosity profiles above the 670-km depth discontinuity. Choosing various subsets of solution 1102, we have also tested the robustness of the results presented, with reference to possible data contaminations due to tectonic deformations. ¿ 2001 American Geophysical Union