Due to the passiveness of the passengers, autonomous cars promise benefits in terms of traffic safety, but also drawbacks in terms of the enjoyment people experience when driving a car themselves. We postulate that both Perceived Traffic Safety and Personal Driving Enjoyment play an important role in people’s acceptance of autonomous cars. After collecting 100 questionnaires and applying a SEM approach, our findings indicate that Personal Driving Enjoyment has a negative influence on the Perceived Enjoyment of autonomous cars and that Perceived Traffic Safety has a positive influence on both their Perceived Usefulness and Perceived Enjoyment. Additionally, both Perceived Usefulness and Perceived Enjoyment were confirmed to positively influence autonomous car acceptance. These findings suggest that autonomous cars should optionally enable people to act as drivers, that manufacturers need to actively manage people’s safety perceptions, and that they also need to emphasize the alternative hedonic benefits that the driverless experience offers.