We study a simple three-lane cellular automaton, based upon the well known NagelSchreckenberg model, and examine the effect of slow cars in such a system. We point out the important parameters defining the shape of the fundamental digram for the three-lane model and compare it to that of a two-lane one, showing the new mode of interactions between lanes. It is possible to reduce the influence of slow cars by choosing an adequate version of the symmetry with respect to lanes.