Knickpoints often form in bedrock rivers in response to base-level lowering. These knickpoints can migrate upstream without dissipating. In the case of alluvial rivers, an impulsive lowering of base level due to, for example, a fault associated with an earthquake or dam removal commonly produces smooth, upstream-progressing degradation; the knickpoint associated with suddenly lowered base level quickly dissipates. Here, however, we use experiments to demonstrate that under conditions of Froude-supercritical flow over an alluvial bed, an instantaneous drop in base level can lead to the formation of upstream-migrating knickpoints that do not dissipate. The base-level fall can generate a single knickpoint, or multiple knickpoints. Multiple knickpoints take the form of cyclic steps, that is, trains of upstream-migrating bedforms, each bounded by a hydraulic jump upstream and downstream. In our experiments, trains of knickpoints were transient, eventually migrating out of the alluvial reach as the bed evolved to a new equilibrium state regulated with lowered base level. Thus the allogenic perturbation of base-level fall can trigger the autogenic generation of multiple knickpoints which are sustained until the alluvial reach recovers a graded state.