Basin-filling strata form casts of the surface topography, preserving records of tectonic events that are the foundation of our understanding of orogen dynamics. Prevailing models for basin formation have proven useful for the interpretation of the vast majority of the sedimentary record, from continental-scale deposystems like foreland basins to fault-bound deposystems along rifts. However, the persistence of high-elevation, hinterland depocenters for millions of years, often without obvious causes of tectonic subsidence, presents a sedimentological conundrum. Non-tectonic topographic depressions on high plateaus, such as those created by landslide or volcanic damming, are finite in volume and likely to be quickly filled over geologic time. The maintenance of depression therefore generally requires the generation of new accommodation. When these enigmatic, long-lived lacustrine depocenters on high plateaus are also paired with adjacent, coeval mantle-derived magmatism, which is evidence of thermodynamic disturbance at the base of the lithosphere, it bears consideration whether these basins are the surface symptoms of deeper mantle dynamics. Few have been recognized as such, including the Miocene Arizaro Basin in the western Puna Plateau, the Tulare Lake basin beneath the southern Sierra Nevada, and the Transylvanian basin beneath the southeastern Carpathians. Two additional candidates are the Bidahochi Basin on the Colorado Plateau, and the Maerguo Basin in Central Tibet. Though apparently difficult to differentiate from other types of basins, the hypothetical dynamic rebound basin may be distinguished based on the unique coincidence of several attributes: (1) an acceleration in subsidence that cannot be explained by flexural loading of a proximal thrust system (i.e. sedimentological characteristics and stratigraphic patterns inconsistent with a proximal thrust system) , (2) anomalous patterns of intrabasinal shortening inconsistent with the regional direction of shortening, (3) rapid basin inversion and exhumation after the end of deposition, and (4) pulse of mantle-derived magmatism at the peak of basin subsidence.