Face recognition systems have been shown to be biased toward certain demographic groups by exhibiting different error rates across gender, age, or ethnicity. Though the imbalance of the training data with respect to these demographics is one cause of this bias, training on artificially balanced groups does not completely mitigate the problem. For deployment, face recognition typically works at operating points allowing very low false match rates and, hence, on the tail of the non-match score distribution. While class balancing can improve the means of these distributions, the aim of our approach is to improve fairness by addressing the behavior in the tail. Particularly, we propose the Demographic-based Supervised Contrastive loss (DeSCon) for face recognition, which relies on a well-designed composition of training batches and demographic-aware pair selection. Our experimental evaluation on both demographically-labeled datasets and standard verification benchmarks shows that DeSCon can improve fairness beyond balancing training datasets while maintaining competitive verification performance. Source code is available upon request.