A method for determination of an optimized evasion trajectory by a safety device or a safety system, in particular a lane change assistance system and/or evasion assistance system, of a motor vehicle, the optimized evasion trajectory being outputted to a vehicle driver, and/or a trajectory of the motor vehicle being optionally partially adapted to the optimized evasion trajectory, by way of the method, the optimized evasion trajectory being determined by optimization of a transverse-dynamic quality factor (J), for which a transverse acceleration (a) and/or a transverse jerk ({dot over (a)}) of the motor vehicle is/are utilized. Also described is a safety device or a safety system, in particular to a lane change assistance system and/or an evasion assistance system for a motor vehicle, a method being executable and/or being executed by the safety device or the safety system.