The field-driven velocity of magnetic domain walls in nanostrips patterned in (Co/Ni) multilayer films with perpendicular anisotropy is studied by magnetooptical microscopy. By applying fields up to 250 mT, two peculiar features are revealed, which are beyond the simple one-dimensional model. First, above wall depinning, a velocity plateau is observed over a 150 mT field range. Then, at large fields, an important increase of velocity occurs. Micromagnetic simulations reproduce this behaviour and underline the nontrivial role of wall structure deformations in the appearance of this complexity. (C) 2011 The Japan Society of Applied Physics