Abstract This paper adopts three approaches to classifying countries by level of constraint, in order to inform the choice of strategies for expanding access to health interventions in different contexts. We find substantial heterogeneity across the 84 low‐income and (all) sub‐Saharan African countries analysed. Poor sub‐Saharan African countries are the most highly constrained; Asian countries, in general, less constrained; and the two Asian giants, China and India, consistently fall above the median. Former Soviet Union countries rank low in terms of governance, but high for health systems variables. Only 10 per cent of the total population of the countries included lives in countries with the greatest constraints. The potential applications of the analysis are discussed, as are the limitations of the cross‐sectional, macro level approach. Copyright © 2003 John Wiley & Sons, Ltd.