The average population health in the last two centuries has improved due to various economic developments, societal transformations and technological progress. An array of socioeconomic, demographic and political variables is tested against health measures such as life expectancy, infant mortality and under-5 mortality in the quest to uncover population health determinants. Consequently, the list of variables claimed to affect health is increasingly growing in the literature and therefore creates a need for a sensitivity analysis. The purpose of this study is to identify and isolate population health determinants which are robust to changes in the choice of explanatory variables by employing a modified version of the extreme-bounds analysis (EBA) developed by Leamer (1983, 1985) and used in Levine and Renelt (1992). A cross-sectional sample set of 95 developed and developing countries is used to facilitate this investigation. Income per capita, female education and access to safe water are among the only few variables found to be robust under the procedure. The EBA results seem to suggest that population health is satisfactorily explained by a small set of key variables. In particular, the robustness of a regional dummy variable indicates that sub-Saharan African countries are extremely disadvantaged in health when compared to other regions or countries. In addition, there is a scope for further research especially towards establishing evidence of causality for these robust variables in the context of determining population health.