The origin of laterally accreted deposits in ancient deep marine successions is often controversial. Indeed, not always do these features imply the occurrence of meanders or high-sinuosity turbidite channels, but they can be generated by other causes, such as sediment-gravity-flow dynamics controlled by the morphology of tectonically confined mini-basins. This work discusses laterally accreted deposits composed of sharp-based, normally graded beds in a very small tectonically controlled mini-basin. These beds, characterized by a well-defined asymmetrical cross-current facies tract, form well-developed lateral-accretion surfaces dipping in directions ranging between W and SW, and perpendicular to the paleocurrents directed towards the N. For this reason, these deposits have always been interpreted as point bars related to meandering channels. A new detailed stratigraphic framework and facies analysis have led to an alternative interpretation, namely that these deposits record lateral deflections of small volume, longitudinally segregated turbidite dense flows against a structurally controlled morphological high. This interpretation is also supported by a comparison to other tectonically controlled turbidite systems that are characterized by higher degrees of efficiency but show similar laterally accreted deposits and cross-current facies tracts.