Flatness based control of the VIENNA-rectifier is sketched. A mathematical averaged model of the rectifier is presented and a flat output is exhibited. Trajectories are planned for an equilibrium regime in order to make clear that it is physically impossible to have at the same time sinusoidal currents, an arbitrary phase-angle between voltage and current space vector, and symmetrically charged output capacitors. Calculating the trajectories, especially of the input variables, from the flat output trajectories and their time derivatives reveals this physical restriction of the system. Three possibilities are presented to overcome the problem. Each of them is a trade-off between the requirements, but all of them guarantee sinusoidal current waveforms. The first one ensures symmetrically charged capacitors, while the second and the third allow for reactive power compensation. Simulations on a switched model illustrate the results.