We study an insurance model characterized by a continuum of risk types, private information and a competitive supply side. We use the model to investigate the welfare effects of discrimination (also known as risk selection). We postulate that a test is available that determines whether an applicant's risk exceeds a treshold. Excluding the highest risks softens adverse selection, but constitutes a welfare loss for the high risks. In contrast to a lemons market intuition, we find that aggregate surplus decreases when risk aversion is high. When risk aversion is low however, discrimination increases aggregate surplus.