Analysts who have concluded that inequality in life expectancy is increasing have generally focused on life expectancy at age 40 to 50. However, we show that among infants, children, and young adults, mortality has been falling more quickly in poorer areas with the result that inequality in mortality has fallen substantially over time. This is an important result given the growing literature showing that good health in childhood predicts better health in adulthood and suggests that today's children are likely to face considerably less inequality in mortality as they age than current adults. We also show that there have been stunning declines in mortality rates for African-Americans between 1990 and 2010, especially for black men. The fact that inequality in mortality has been moving in opposite directions for the young and the old, as well as for some segments of the African-American and non-African-American populations argues against a single driver of trends in mortality inequality, such as rising income inequality. Rather, there are likely to be multiple specific causes affecting different segments of the population. We show that the differential timing of smoking reductions among the rich and the poor can explain a significant fraction of the current increase in mortality inequality in older cohorts.