We have investigated numerically the field-driven propagation of perpendicularly magnetized ferromagnetic layers. It was then compared to the historical one-dimensional domain wall (DW) propagation model widely used in spintronics studies of magnetic nanostructures. In the particular regime of layer thickness (h) of the order of the exchange length, anomalous velocity peaks appear in the precessional regime, their shape and position shifting with h. This has also been observed experimentally. Analyses of the simulations show a distinct correlation between the curvature of the DW and the twist of the magnetization vector within it, and the velocity peak. Associating a phenomenological description of this twist with a four-coordinate DW propagation model, we reproduce very well these kinks and show that they result from the torque exerted by the stray field created by the domains on the twisted magnetization. The position of the peaks is well predicted from the DW's first flexural mode frequency, and depends strongly on the layer thickness. Comparison of the proposed model to DW propagation data obtained on dilute semiconductor ferromagnets GaMnAs and GaMnAsP sheds light on the origin of the measured peaks.