We present the general model MOBIL ("Minimizing Overall Braking Induced by Lane Changes") to derive lane-changing rules for a wide class of car-following models. Both the utility of a given lane and the risk associated with lane changes is determined in terms of longitudinal accelerations calculated with microscopic traffic models. This allows for the formulation of compact and general safety and incentive criteria both for symmetric and asymmetric passing rules. Moreover, anticipative elements and the crucial influence of velocity differences of the longitudinal traffic models are automatically transferred to the lane-changing rules. While the safety criterion prevents critical lane changes and collisions, the incentive criterion takes into account not only the own advantage but also the (dis-)advantages of other drivers associated with a lane change via a "politeness factor". The parameter allows to vary the motivation for lane-changing from purely egoistic to a more cooperative driving behavior. This novel feature allows first to prevent change lanes for a marginal advantage if this obstructs other drivers, and, second, to let a "pushy" driver induce a lane change of a slower driver ahead in order to be no longer obstructed. In a more general context, we show that applying the MOBIL concept without politeness to simple car-following models and cellular automata results in lane changing models already known in the literature.