Should insurance prices vary with age? I consider competitive markets for lemons where a signal (e.g., age) partitions consumers (e.g., young and old). I study the continuum of policies from zero price-discrimination (zero- PD, equal prices) to full-PD (no restrictions). Restricting PD can increases welfare if high-cost markets exhibit greater adverse selection, or when the high-cost market “unravels.” I characterize optimal PD, and show how it is affected by changes in cost. In a calibration, optimal PD increases welfare by about $30/person-year. I extend the model to arbitrary signal structures, behavioral consumers, a monopolized industry, and multi-product firms.