Various, but related, models have been proposed to explain the architectural arrangement of channel stacking patterns in avulsion-dominated alluvial sequences. The early models published by Leeder, Allen, and Bridge (LAB) addressed the role of changes in sedimentation rate (a proxy for subsidence rate) as a control on stacking patterns. The models decouple avulsion frequency from sedimentation rates, resulting in an inverse relationship between stacking density (or interconnectedness) and sedimentation rates. A key element missing from these models is the likely dependence of avulsion frequency on local sedimentation rate within the active channel belt. We consider a simple model whereby avulsion takes place only when a minimum, critical, relief is developed between a channel bank and the adjacent flood plain. If avulsion frequency increases at rates slower than the increase in sedimentation rate, then stacking density increases with decreasing sedimentation rate, similar to that predicted by the LAB models. However, if avulsion frequency increases linearly with sedimentation rate, then there is no change in stacking pattern with changes in sedimentation rate. If avulsion frequency increases faster than sedimentation rates, as seen in some data sets, then stacking patterns become more dense with increasing sedimentation rates, a result that is the exact opposite of that predicted by the LAB models. Therefore sensitive dependence on the relationship between avulsion frequency and sedimentation rate calls into question the veracity of some previous interpretations of relative subsidence made in alluvial architecture studies. We provide an alternative, simple geometric model that links changes in subsidence rate to downstream rate of change in stacking pattern as seen in three dimensions within sedimentary basins. Other controls that are considered include: the geometry of subsidence; whether avulsions take place locally along a river or regionally affect the basin; whether local sedimentation rate or flow depth controls the thickness of sand bodies; and the exact relationship between avulsion frequency and sedimentation rate. The primary result of the model is that subsidence strongly influences the rate at which alluvial architecture changes in the downstream direction, but other controls dictate whether the stacking pattern becomes more dense or less dense downstream. Hence, we suggest that subsidence exerts an influence on stacking patterns not necessarily evident in individual vertical sections, but may be recorded in three dimensions as downstream changes in alluvial architecture. Unfortunately any model of alluvial architecture in avulsion-dominated sequences is limited by our lack of understanding of the processes controlling avulsion. As a result any model of alluvial stacking patterns is at best a working hypothesis that should not be taken as proof of changes in tectonic subsidence rates or sea-level changes.