To develop a driver assistance system with the goal to increase driving efficiency, we aimed at understanding unassisted driving behaviour. With this knowledge, we will then be able to estimate the potential of the assistance system to support drivers in avoiding unnecessary deceleration and acceleration when approaching traffic lights and to estimate the amount of influence the driver assistance system could have on normal driving. Efficient driving was defined as driving behaviour that leads to reduced fuel consumption and emissions. In a driving simulator experiment with twelve participants and a within-subjects design, drivers approached intersections while the traffic light was either solid green or solid red, or changed from red to green or from green to red during the approach. In addition, we varied whether there was a lead vehicle present and manipulated visibility through the presence or absence of fog. Driving speed, acceleration and pedal usage were analysed and interpreted due to their relation with fuel consumptions and emissions, which is well known from the literature. Participants avoided strong accelerations and decelerations when approaching a solid green traffic light compared to a changing red to green traffic light. Speed was reduced earlier, when the traffic light was solid red compared to when the traffic light changed from green to red. Higher visibility in the non-fog conditions compared to the fog condition was only an advantage in terms of more efficient driving behaviour when the traffic light phase did not change during the approach. The potential for improvements in driving efficiency was higher when drivers were in free driving compared to when following a lead vehicle. We propose that approaching traffic light intersections takes place in three phases: an orientation, a preparation and a realisation phase. A driver assistance system is expected to improve drivers' anticipation of the driving scene and could recommend efficient driving behaviour in all three phases.