Abstract Can sedimentary topographic relief (here termed uneven sedimentation) explain the enigmatic early initiation of salt minibasins at rifted continental margins when the sediment fill is less dense than the underlying salt? Using isostatic balancing arguments for compacting sediments, we first demonstrate that minibasin-scale thickness variations in a weak sedimentary overburden can cause lateral pressure differences large enough to initiate salt minibasins. These contribute toward the minibasin attaining the Rayleigh–Taylor threshold, the point at which sediments sink into an underlying salt layer. Secondly, using two-dimensional plane-strain finite element models, we show that uneven sediment loading on a viscous salt channel can initiate salt minibasins even when sediments have finite strength. Uneven sedimentation (sedimentary topographic relief) is idealized in the models as uniform aggradation of compacting sediment with a superimposed smooth sinusoidal topographic perturbation, wavelength λ , maximum height h l . Our main goal is to estimate the minimum duration that uneven sedimentation must persist, t P , such that the strength of the sediments is overcome and the minibasin continues to develop and mature (a successful minibasin) when uneven sedimentation is replaced by uniform aggradation. We investigate models with widths, W , equal to λ (confined salt models), and greater than λ (unconfined salt models). Our results suggest that for models that develop successful minibasins there is an optimal value of λ , λ OPT , for which t RT , the time to attain the theoretical Rayleigh–Taylor threshold based on isostasy arguments, and t P are the smallest. This wavelength selection exists when the sediments have moderate (e.g., shale) to high (e.g., carbonates) density but is not prominent for low density sediments. For confined salt models at λ OPT , t P varies from 8.0 to 2.25 Ma for low to high density sediments, respectively, when h l ranges from 40 to 80 m. In unconfined models, where salt can be expelled over larger distances than λ , t P ranges from 7 to 1.5 Ma. For a given sediment density and compaction model, there is a lower limit of λ below which uneven sedimentation alone does not initiate minibasins. However, successful minibasins develop over a wider range of λ in unconfined models and when W≫λ , uneven sedimentation in one location can indirectly lead to the development of outboard basins. Uneven sediment may alternatively be deposited on a uniformly thick, compacting pre-kinematic sediment layer. Under these circumstances t P is further reduced to 9.0–0.5 Ma depending on the density of the sediments. Weak in-plane contraction can further reduce t P to 3.5–0.375 Ma even for low density sediments. Under optimal conditions a period of uneven sedimentation of this type in an otherwise uniformly aggrading sequence need only have a topographic amplitude of 40–80 m and persist for 0.05–2 Ma in order to seed the development of a successful minibasin. Our idealized uneven sedimentation model is interpreted as a proxy for channel–levee systems, turbidite lobe complexes, and/or lateral sediment density variations that cause equivalent sediment loading, and which occur both in the down-dip and along-strike directions of a rifted margin.