anomalous curves are found in particular for samples (B) and (C), for which the sign of the speed asymmetry would suggest that the value of $D$ is either vanishing (for (B)) or opposite (for (C)) to the one of sample (D). This indicates that in the creep regime extreme care should be taken when extracting information on the DMI sign and amplitude simply on the basis of the asymmetry (or lack of asymmetry) of the Kerr microscopy differential images. Before assessing about $D$, the full speed *vs.* $H_{x}$ curves should be examined and compared with the curves predicted by the existing theoretical models.

In order to verify the role of the DW pinning on the speed *vs.* $H_{x}$ field, we have repeated the field-dependent measurements for larger values of the $H_{z}$ fields, bringing the domain wall velocities to a regime ($\gg$ 1m/s) where the propagation is much less sensitive to the pinning generated by local variations of the anisotropy field. Pulsed $H_{z}$ fields up to 200mT and duration down to 20ns were obtained using a $50\,\upmu$m wide microcoil coupled to a fast current pulse generator [@Mackay2000]. The results reported in Figure \[fig:speed\_H\_flow\] for samples (A) to (D) show that in 