Abstract: Average living standards are converging among developing countries and faster growing economies see more progress against poverty. Yet we do not find poverty convergence; countries starting with higher poverty rates do not see higher proportionate rates of poverty reduction. The paper tries to explain why. Analysis of a new dataset suggests that, at given mean consumption, high initial poverty has an adverse effect on consumption growth and also makes growth less poverty-reducing. Thus, for many poor countries, the growth advantage of starting out with a low mean is lost due to a high incidence of poverty. (JEL D63, I31, I32, O15)