We argue that canonical heterogeneous-agent economies are unable to jointly account for the observed concentration of consumption, labor income, wealth, and capital income at the top. We first provide empirical evidence that the distributions of these four variables exhibit asymptotic power-law behavior with a strict ranking of upper tail inequality in that order, from least to most unequal. This finding directly contradicts a central implication of precautionary savings models, in which consumption and capital income are asymptotically linear in, and therefore as concentrated at the top as, wealth. Mechanisms addressing the wealth concentration puzzle through return heterogeneity thus lead to a mirror consumption concentration puzzle. We show analytically and quantitatively that accounting simultaneously for the observed concentration of consumption, wealth, and capital income requires a combination of non-homothetic wealth-dependent preferences and scale-dependent returns to capital, and we identify the strength of these two mechanisms from the values of the Pareto tail coefficients. Finally, matching all four tails matters for determining the long-run elasticity of savings that governs the revenue-maximizing capital tax rate.