What controls the architecture of drainage networks is a fundamental question in geomorphology. Recent work has elucidated the mechanisms of drainage network development in steadily uplifting landscapes, but the controls on drainage-network morphology in transient landscapes are relatively unknown. In this paper we exploit natural experiments in drainage network development in incised Plio-Quaternary alluvial fan surfaces in order to understand and quantify drainage network development in highly transient landscapes, i.e. initially unincised low-relief surfaces that experience a pulse of rapid base-level drop followed by relative base-level stasis. Parallel drainage networks formed on incised alluvial-fan surfaces tend to have a drainage spacing that is approximately proportional to the magnitude of the base-level drop. Numerical experiments suggest that this observed relationship between the magnitude of base-level drop and mean drainage spacing is the result of feedbacks among the depth of valley incision, mass wasting and nonlinear increases in the rate of colluvial sediment transport with slope gradient on steep valley side slopes that lead to increasingly wide valleys in cases of larger base-level drop. We identify a threshold magnitude of base-level drop above which side slopes lengthen sufficiently to promote increases in contributing area and fluvial incision rates that lead to branching and encourage drainage networks to transition from systems of first-order valleys to systems of higher-order, branching valleys. The headward growth of these branching tributaries prevents the development of adjacent, ephemeral drainages and promotes a higher mean valley spacing relative to cases in which tributaries do not form. Model results offer additional insights into the response of initially unincised landscapes to rapid base-level drop and provide a preliminary basis for understanding how varying amounts of base-level change influence valley network morphology.