Digital elevation models (DEMs) are the primary source for 2D hydrological modelling. Most approaches require a sink-free DEM, because standard flow tracing methods stops at the bottom of sinks. Sinks are commonly removed by sink filling, raising elevation values in the sink to the spill point. This is equivalent to filling a sink with water until the water overflows. The modifications introduced to the DEM by sink filling can be substantial. Sink filling assumes that elevation values are too low, and raises elevation values until the DEM is completely drained. DEMs obtained with remote sensing (radar, LiDAR, stereo imagery) have systematically too high and not too low values. Thus selected elevation values should be lowered rather than raised in order to drain a DEM completely. This method is known as carving, where a channel is carved into the DEM. The minimum impact approach investigates each sink and determines the impact of filling and carving. Each sink is then removed with the method causing less modifications. Here we present a new minimum impact approach that further reduces the amount of modifications. Each sink is removed by a combination of filling and carving. The best combination for a given sink is the combination of filling the sink up to a certain level and carving out a channel from that level that causes the least modifications to the DEM. Flow directions for carving are determined with a least cost path search. We compare the amount of modifications introduced by different methods and the resultant surface flow accumulations. The new method is implemented in the GRASS GIS module r.hydrodem. The hydrologically conditioned DEM can be used with any hydrological modelling software.