The relative importance of crustal thickening, lithospheric delamination, and climate change in driving surface uplift and the associated changes in accommodation space and depositional facies in the adjacent foreland basin in the central Andes has been a topic of vigorous debate over the past decade. Interpretation of structural, geochemical, geomorphic, and geobiologic field data has led to two proposed end-member Tertiary surface uplift scenarios for the Eastern Cordillera and Subandes in the vicinity of the Bolivian orocline. A “gradual uplift” model proposes that the rate of surface uplift has been relatively steady since deformation propagated into the Eastern Cordillera during the late Eocene. In this scenario, the mean elevation of the region was >2 km above mean sea level (msl) by the late Miocene or earlier. Alternatively, a “rapid uplift” model suggests that the mean elevation of the Altiplano was <1 km above msl, and the peaks of the Eastern Cordillera were more than 2 km below their modern elevations until rapid uplift began ca. 10 Ma. Determining which of these uplift scenarios is most consistent with the stratigraphic record is complicated by the potentially confounding effects of global climate changes and lithospheric delamination in the stratigraphic record. In this study, we use a coupled mountain-belt–sediment-transport model to predict the foreland basin stratigraphic response to these end-member surface uplift scenarios. Our model results indicate that the location and height of the migrating deformation front play the dominant roles in controlling changes in accommodation space and grain size within the foreland basin. Changes in accommodation space and rates of sediment supply related to climate change and lithospheric delamination play secondary roles. Our results support the conclusion that the Eastern Cordillera likely gained most of its modern elevation prior to 10 Ma, in contrast with recent proposals that most of the modern elevation was obtained during the late Miocene. This conclusion is consistent with the most comprehensive paleoaltimetric analysis of the region to date.