Veiling among Muslim women is modeled as a commitment mechanism that limits temptation to deviate from religious norms of behavior. The analysis suggests that veiling is a strategy for integration, enabling women to take up outside economic opportunities while preserving their reputation within the community. This accounts for puzzling features of the new veiling movement since the 1970s. Veiling also has surprising effects on the intergenerational transmission of values. Compulsory veiling laws can lead to a decline in religiosity. Bans on veiling can inhibit social integration and increase religiosity.