Inversion of the fundamental mode of the Rayleigh wave dispersion curve does not provide a unique solution and the choice of the parameterization (number of layers, range of velocity, and thickness values for the layers) is of prime importance for obtaining reliable results. We analyzed shear-wave velocity profiles derived from borehole tests at 10 sites where soil layers overlay bedrock in various geologic contexts. One to three seismic layers with linear velocity laws could model all of them. Three synthetic models defined from this preliminary study were used to understand the influence of parameterization on the dispersion curve inversion. This analysis resulted in the definition of a two-step inversion procedure for sites exhibiting a strong impedance contrast. In the first step, the dispersion curve is inverted with an increasing number of layers over half space. The evolution of the minimum misfit and bedrock depth with number of layers allows the estimation of the true bedrock depth range. In the second step, this information is introduced in inversions with linear velocity laws. Synthetic tests showed that applying this procedure requires the dispersion curve over a frequency range from to , where is the site resonance frequency. The strategy was tested on two real cases for which Rayleigh wave dispersion curves were measured over this frequency range using passive and active seismic methods. The strategy was successful at the first site, while the bedrock depth was overestimated by 15% at the second site, probably resulting from the existence of a higher mode affecting the dispersion curve at low frequency.