Climate-economics models often assume that middle-income countries' per capita incomes will catch up with those of today's high income countries, while low-income countries will lag behind. This choice underrates the least developed countries' chance to escape poverty. The consequences in terms of the resulting policy advice are stark: assumed slow growth for the poorest countries means lower projected business-as-usual emissions and, as a consequence, much weaker emissions reduction goals. But what if low-income countries grow more quickly, as China and India have? This article reviews current practices in modelling income growth in integrated assessment models of climate and economy, provides an illustration of the impact that more optimistic economic development expectations would have on emissions mitigation targets, discusses different policy options and concludes with recommendations for integrated assessment modellers.