One of the greatest challenges in the field of hillslope hydrology is conceptualizing and parameterizing the effects of lateral preferential flow. Our current physically based and conceptual models often ignore such behavior. However, for addressing issues of land use change, water quality, and other predictions where flow amount and components of flow are imperative, dominant runoff processes like preferential subsurface flow need to be accounted for in the model structure. This paper provides a new approach to formalize the qualitative yet complex explanation of preferential flow into a numerical model structure. We base our examples on field studies of the well-studied Maimai watershed (New Zealand). We then use the model as a learning tool for improved clarity into the old water paradox and reasons for the seemingly contradictory findings of lateral preferential flow of old water where applied line sources of tracer appear very quickly in the stream following application. We evaluate the model with multiple criteria, including ability to capture flow, hydrograph composition, and tracer breakthrough. We generate output ensembles with different pipe network geometries for model calibration and validation analysis. Surprisingly, the range of runoff response among the ensembles is narrow, indicating insensitivity to specific pipe placement. Our new model structure shows that high transport velocities for artificial line source tracers can be reconciled with the dominance of preevent water during runoff events even when lateral pipe flow dominates response. The work suggests overall that preferential flow can be parameterized within a process-based model structure via the structured dialog between experimentalist and modeler.