Carrier screens are widely used in medical genetics to prevent rare genetic disorders. Current detection methods are based on serial processing which is slow and expensive. Here, we discuss a highly efficient compressed sensing approach for ultra-high throughput carrier screens, and highlight both similarities and unique features of our setting compared to the standard compressed sensing framework. Using simulations, we demonstrate the power of compressed carrier screens in a real scenario - finding carriers for rare genetic diseases in Ashkenazi Jews, a population that has well established wide-scale carrier screen programs. We also compare the decoding performance of two typical reconstruction approaches in compressed sensing - GPSR and Belief Propagation. Our results show that Belief Propagation confers better decoding performance in the current application.