The eradication of child undernutrition and extreme poverty are important objectives for most societies. Countries with higher national incomes usually improve in both dimensions, but not always at the same rate. Using quantile regression, we show that poverty rates tend to decline with increased income at a roughly constant elasticity. In contrast, while the prevalence of child underweight declines at that same elasticity where it is most widespread, the elasticity becomes smaller as underweight becomes less prevalent. This finding suggests a need for increasingly targeted interventions to achieve a given reduction in undernutrition as its prevalence declines.