An income growth pattern is pro-poor if it reduces a (chosen) measure of poverty by more than if all incomes were growing equiproportionately. Inequality reduction is not sufficient for pro-poorness. In this paper, we explore the nexus between pro-poorness, growth, and inequality in some detail using simulations involving the displaced lognormal, Singh–Maddala, and Dagum distributions. For empirically relevant parameter estimates, distributional change preserving the functional form of each of these three-parameter distributions is often either pro-poor and inequality reducing, or pro-rich and inequality exacerbating, but it is also possible for pro-rich growth to be inequality reducing. There is some capacity for each of these distributions to show trickle effects (weak pro-richness) along with inequality-reducing growth, but virtually no possibility of pro-poorness for growth which increases overall inequality. Implications are considered.