Coarse-grained strata deposited on continental shelves and epeiric seas in some tens of meters' water depth are conventionally ascribed simply to storms of varying intensity which interrupted the settling out of suspended mud. Surprisingly, the possibility of tsunamis is virtually never evaluated even though they might, indeed should, have been common in many regions. Portions of the Middle Cambrian La Laja Formation of the Argentine Precordillera formed in such a submerged epeiric platform or shelf. They comprise a suite of three limestone facies: variably argillaceous burrowed mudstone, bioclastic grainstone, and intraclastic conglomerate composed of pieces of mudstone including cemented haloes around burrows. Sporadically developed eocrinoid meadows and trilobite populations are recorded respectively by disarticulated ossicles and usually broken sclerites. The latter indicate that, generally, exoskeletons became fragmented by repeated bottom turbulence. Hence, the mudstones and grainstones show that, before stabilization by calcite cementation which began beneath the sediment–water interface and away from burrow margins, physical reworking of the surface sediment by storms was so frequent that it did not leave a specific signature of individual events. By contrast, scattered lenticular beds of intraclastic conglomerate were due to anomalous, brief episodes of deep scour and strong oscillatory flow from powerful wave action. These conglomerates then escaped subsequent reworking. Because they are abruptly interbedded and encased within uniform mudstone, and there are no stratigraphic patterns, allochthonous material, or unconformities to indicate sea-level fluctuation, the events that created the conglomerates were more likely tsunamis, not storms. They could have been unleashed by faulting elsewhere on the shelf or rifting beyond the shelf margin to the (present-day) west to southwest. Those originating in the rift basin may have been diffracted by marginal shoals and attenuated by the shallowness of the platform which caused the waves to break some distance offshore. In any case, the study area was not affected by backwash. Recognition of tsunami-laid beds urges a reexamination of the standard tempestite paradigm with its use of coarse-grained strata as a simple measure of storm frequency and intensity.