Numerous health insurers offer bonus programmes that score customers’ health behaviour, and car insurers offer telematics tariffs that score driving behaviour. In many countries, however, only a minority of customers participate in these programmes. In a population-representative survey of private households in Germany (N = 2,215), we study the acceptance of the criteria (features) on which the scoring programmes are based: the features for driver scoring (speed, texting while driving, time of driving, area of driving, accelerating and braking behaviour, respectively) and for health scoring (walking distance per day, sleeping hours per night, alcohol consumption, weight, participation in recommended cancer screenings, smoking status). In a second step, we model participants’ acceptance of both programmes with regard to the underlying feature acceptance. We find that insurers in Germany rarely use the features which the participants consider to be the most relevant and justifiable, that is, smoking status for health scoring and smartphone use for driver scoring. Heuristic models (fast-and-frugal trees) show that programme acceptance depends on the acceptance of a few features. These models can help to understand customers’ preferences and to design scoring programmes that are based on scientific evidence regarding behaviours and factors associated with good health and safe driving and are thus more likely to be accepted.