Digital flow networks derived from digital elevation models (DEMs) sensitively react to errors due to measurement, data processing and data representation. Since high-resolution DEMs are increasingly used in geomorphological and hydrological research, automated and semi-automated procedures to reduce the impact of such errors on flow networks are required. One such technique is stream-carving, a hydrological conditioning technique to ensure drainage connectivity in DEMs towards the DEM edges. Here we test and modify a state-of-the-art carving algorithm for flow network derivation in a low-relief, agricultural landscape characterized by a large number of spurious, topographic depressions. Our results show that the investigated algorithm reconstructs a benchmark network insufficiently in terms of carving energy, distance and a topological network measure. The modification to the algorithm that performed best, combines the least-cost auxiliary topography (LCAT) carving with a constrained breaching algorithm that explicitly takes automatically identified channel locations into account. We applied our methods to a low relief landscape, but the results can be transferred to flow network derivation of DEMs in moderate to mountainous relief in situations where the valley bottom is broad and flat and precise derivations of the flow networks are needed. Copyright © 2013 John Wiley & Sons, Ltd.