Seismic attenuation and velocity are two coupled parameters with different sensitivities. We propose to explicitly use the dispersion relation during full waveform inversion. In a first step, a classical visco-acoustic inversion is applied for a fixed quality factor, then a subsequent modified full waveform inversion leads to a faster convergence compared to the standard scheme. The approach is validated on a simple 2D synthetic data set mainly dominated by transmitted waves. The new scheme is an alternative to the Hessian-based strategy.