Datafication offers several benefits to the insurance sector, but the success of data-driven insurance depends very much on customer acceptance. Thus, this study examines factors that influence customer acceptance of data-driven car and health insurance. These two types of data-driven insurance are based on fitness and driving data, both of which require access to sensor and geo-localization data. The results of an online study with 217 participants using advertisements for data-driven insurances showed that highlighting monetary incentives leads to a higher acceptance than highlighting health or safety incentives. Data-driven insurances allow for individualized tariffs, and accordingly, it is more likely that people who rate their driving skills above-average will take out a datadriven car insurance. Privacy concerns are another important influence factor. The findings demonstrate that customer acceptance of data-driven insurance can be influenced to some extent by framing decision-relevant information material.