Distinguishing between forced and unforced regressive strata is important for identification of systems tracts, prediction of sediment bypass, and reconstruction of relative sea-level histories. Conventional sequence stratigraphic models distinguish between forced and unforced regressive strata through the presence of aggradational topset (no aggradation during forced regression) and style of shoreline trajectory (descending in forced regressive strata and flat to rising in unforced regressive strata). However, because present models contain implicit assumptions about sediment supply and the response of coastal-plain and fluvial deposystems to falling and rising relative sea level, it is probable that these two scenarios are an oversimplification of a more complex reality. This work investigates how topset aggradation might develop during relative sea-level fall using 1264 runs from a simple diffusional stratigraphic forward model. Topset aggradation is characterized for each model run by a topset/foreset volume ratio (t/f ratio). When topset strata are present the t/f ratio is > 0, when no topset strata are present the t/f ratio is zero. Multiple two-dimensional model runs (0.4 or 2 My duration, and constant sediment supply and discharge rates representative of medium-size river systems) suggest that sediment transport rate may be a key control on topset aggradation. Modeling a range of sediment transport rates for amplitudes of relative sea-level fall from 0 to 100 m shows that with relatively high rates of sediment transport, multiple model runs create strata with t/f ratios up to 0.08. Conversely, relatively low sediment transport rates lead to higher volumes of topset deposition reflected by t/f ratios ranging from 0.10 to 0.37. However, critically, high sediment transport with no relative sea-level fall leads to topset aggradation very similar to that resulting from low sediment transport and high-amplitude relative sea-level fall. This is an example of non-uniqueness, showing that topset aggradation can occur during falling relative sea level as well as steady to rising relative sea level, depending on rates of sediment transport. This result has been tested and verified with different rates of relative sea-level fall and with additional three-dimensional model runs, including runs in a different model. The results suggest that backstripped shoreline trajectories are likely to be a more reliable method of distinguishing forced from unforced regression, and that interpretation and prediction of sediment bypass history may be more complicated than current sequence stratigraphic models suggest.