Spurious pits in grid digital elevation models are often removed by filling them up to the level of their outflow point. Recently, an alternative approach called carving has been proposed to suppress each single pit by creating a descending path from it to the nearest point having a lower elevation value. In this paper, we propose an optimal method combining both approaches and minimizing the cost necessary for transforming an input digital elevation model into a pitless digital elevation model. The cost of this transformation is defined by the sum of the altitude differences between the input and output pitless digital elevation models. Experimental results are presented for a digital elevation model of continental Europe with a grid cell size of 250 m.