This paper applies a new methodology to the study of hospital efficiency and quality of care. Using a data set of hospitals from several states, we jointly evaluate desirable hospital patient care output (e.g., patient stays) and the simultaneous undesirable output (e.g., risk-adjusted patient mortality) that occurs. With a DEA based approach under two different sets of assumptions, we are able to include multiple quality indicators as outputs. The results show that lower technical efficiency is associated with poorer risk-adjusted quality outcomes in the study hospitals. They are consistent with other studies linking poor quality outcomes to higher cost.