The dependence of rotational relaxation rates on the speed of absorbing molecules has been studied by millimeterwave coherent transients for the J,K=1,1-2,1 rotational transition of methyl fluoride (CH3F). A new phenomenological model used to describe such a speed- dependence has been introduced. It leads to a quite simple analytical expression for time-domain transient signals, the Fourier transform of which corresponds to the frequency-domain line shape (speed-dependent Voigt profile). The investigations were carried out on mixtures of CH3F with He, Ar, Xe, H-2, D-2, N-2, and O-2, yielding parameters which characterize the speed dependence of the observed decay rates and its pressure and temperature dependence. Special emphasis was given to the key role of the mass ratio of collision partners which clearly allowed the relation of the observed nonexponential decay behavior to collisional effects. However, the observations cannot be explained exclusively with consideration of speed-dependent rates, but must also be discussed with reference to velocity-changing collisions. The observed temperature dependence of the rates may allow discrimination between these two different collisional effects which lead to departures from Voigt profile line shapes.