Modeling of flow and solutional processes within networks of interconnected conduits in limestone aquifers indicates that enlargement occurs very selectively during the early stages of karst aquifer development under laminar flow. If initial flow paths are uniform in size, almost all enlargement occurs along a single set of connected conduits that lie along a direct path between recharge and discharge locations and are aligned along the hydraulic gradient. With a sufficiently large variation in initial aperture widths, enlargement occurs along the flow path offering the least resistance to flow, but since flow rates in laminar flow are proportional to the fourth power of diameter but only linearly proportional to hydraulic gradient, the preferentially enlarged set of fractures may follow an indirect path. Results disfavor earlier suggestions that nonselective cave patterns result from artesian flows (at least under laminar flow conditions) and that all passages should be competitive until the onset of turbulent flow.