In the light of the recent high quality data of the cosmic microwave background anisotropies, several estimations of cosmological parameters have been published. We study to what extent these estimations depend on assumptions about the initial conditions of the cosmological perturbations, which are usually supposed to be adiabatic. We show that, for more generic initial conditions, not only the best fit values are very different but the allowed parameter range enlarges dramatically. This raises the question which cosmological information (matter content of the Universe vs physics of inflation) can be reliably extracted from these data.