Some medical services have long generated deep moral controversy within the medical profession as well as in broader society and have led to conscientious refusals by some physicians to provide those services to their patients. More recently, pharmacists in a number of states have refused on grounds of conscience to fill legal prescriptions for their customers. This paper assesses these controversies. First, I offer a brief account of the basis and limits of the claim to be free to act on one's conscience. Second, I sketch an account of the basis of the medical and pharmacy professions' responsibilities and the process by which they are specified and change over time. Third, I then set out and defend what I call the "conventional compromise" as a reasonable accommodation to conflicts between these professions' responsibilities and the moral integrity of their individual members. Finally, I take up and reject the complicity objection to the conventional compromise. Put together, this provides my answer to the question posed in the title of my paper: "Conscientious refusal by physicians and pharmacists: who is obligated to do what, and why?".