A giant bed of ash and pumice (≤ 80 m thick and covering >300 km2) in central Mexico demonstrates that thick clastic beds lacking sedimentary structures can aggrade incrementally from the base of sustained density currents. Like similar giant beds with matrix-supported clasts elsewhere, it had been interpreted as having formed en masse from a giant flow with high yield strength. However, intergradational compositional zones within the bed record changes in the material supplied at the source over time; the zones show that the density current was initially topographically restricted and that valleys progressively filled with deposit so that later parts of same density current were able to pass over and bury successively higher ground. This example provides a key to understanding the origin of massive parts of ignimbrites, megaturbidites, lahar deposits, and some debris-flow deposits. It shows that (1) an absence of sedimentary structures cannot be used to infer near-instantaneous deposition by en masse “freezing” or “collapse” of a giant flow, and (2) the thickness and vertical organization of a giant bed tell us little about thickness, vertical organization, and rheology of the current that produced it.