This paper presents a numerical model study simulating the early karstification of a single conduit embedded in a fissured system. A hybrid continuum-discrete pipe flow model (CAVE) is used for the modeling. The effects of coupling of the two flow systems on type and duration of early karstification are studied for different boundary conditions. Assuming fixed head boundaries at both ends of the conduit, coupling of the two flow systems via exchange flow between the conduit and the fissured system leads to an enhanced evolution of the conduit. This effect is valid over a wide range of initial conduit diameters, and karstification is accelerated by a factor of about 100 as compared to the case of no exchange flow. Parameter studies reveal the influence of the exchange coefficient and of the hydraulic conductivity of the fissured system on the development time for the conduit. In a second scenario the upstream fixed head boundary is switched to a fixed flow boundary at a specified flow rate during the evolution, limiting the amount of water draining toward the evolving conduit. Depending on the flow rate specified, conduit evolution may be slowed down or greatly impaired if exchange flow is considered.