As spectacular mortality reductions have occurred in all developing nations at all national income levels, the epidemiologic transition theory suggests that cause-of-mortality patterns should shift from communicable diseases especially prevalent among infants and children to problems resulting from non-communicable conditions at older ages. Global estimates confirm this expectation, and mortality from these latter conditions has become predominant worldwide, leading some observers to argue for a corresponding shift in the public health agenda. In this paper, we nuance this finding by studying the important poverty-gradient concealed in the global estimates. Our results demonstrate the remaining cause-of-death disparities between the world's poorest and richest populations. We find that the poorest population (1st quintile) experiences higher mortality than the richest population (5th quintile) in each of the three main groups of mortality causes but that the excess mortality of the poorest population is mostly due to the higher incidence of communicable diseases (77% of excess deaths). Overall, those diseases only account for 34.2% of deaths in the world but still dominate mortality causes among the poorest 20% of the world population (58.6% of all deaths). Moreover, these results appear robust to alternative estimates of the international distribution of the world's poorest people. While recognizing the emerging agenda of the non-communicable conditions, we thus underscore the "unfinished agenda" of communicable diseases in many countries. As populations affected by these diseases are predominantly among the poorer, equity considerations should caution against a premature shift away from these diseases.