In existing models of alluvial architecture it is typically assumed that mean avulsion frequency is independent of sedimentation rate. However, if avulsion is driven by superelevation of a river bed above its surrounding flood plain, one might expect avulsion rate to increase with sedimentation rate. We have carried out a series of experiments with laboratory-scale fluvial fans in which we measured the frequency of apical avulsions as a function of mean sedimentation rate on the fan. Avulsion frequency increased strongly with increasing sedimentation rate and then stabilized as mass flows began to influence deposition. In the regime of increasing avulsion frequency, the added volume of sediment needed to trigger an avulsion decreased with increasing sedimentation rate. Although our experimental results cannot simply be scaled up to natural rivers, they suggest the possibility of coupling between avulsion frequency and sedimentation rate that would be strong enough to change qualitatively the results of existing models of alluvial architecture. These models should be applied with caution until avulsion mechanics are better understood.