The origin of massive sands in turbidite successions has commonly been attributed to the rapid dumping of sand due to flow unsteadiness in collapsing, single surge-type, high-density turbidity currents. The general applicability of this model is questioned here, and we propose that rapid deposition of massive sands also occurs due to non-uniformity in prolonged, quasi-steady high-density turbidity currents. We attempt to eliminate ambiguity in the use of the terms ‘deceleration’and ‘unsteadiness’with respect to non-uniform sediment gravity flows, and stress that, as with any particulate current, unsteadiness is not a prerequisite of sediment deposition. We propose a mechanism of gradual aggradation of sand beneath a sustained steady or quasi-steady current, and upward-migration of a depositional flow boundary that is dominated by grain hyperconcentration and hindered settling. Formation of tractional structures is prevented by the absence of a sharp rheological interface between the lowest parts of the flow and the just-formed dewatering deposit. Deposition continues as long as the downward grain flux to the depositional flow boundary is balanced by grain supply from above or from upcurrent. Massive sand deposited in this way is not, strictly, a result of ‘direct suspension sedimentation’in that it is characterized by grain interactions, hindered settling, shear and, possibly, by interlocking of grains. The thickness of the resulting massive sand bears no relation to the thickness of the parental current, and the vertical variation within the deposit may reveal little about the vertical structure of the current, even during deposition. Thin, normally graded tops or mud drapes represent the eventual waning of sustained currents.