Concave-shaped surfaces have been prepared on 6H-SiC(0001) substrates by exposing troughs, prepared by dimple grinding of flat SiC surfaces, to H₂ at high temperature. The morphological changes occurring under this H₂ etching were studied using scanning electron microscopy (SEM), atomic force microscopy (AFM) and ultrahigh vacuum scanning tunnelling microscopy (UHV-STM). Already after heating in H₂ at 1600 ^°C for 20 min, morphological changes are observed and heating in H₂ at 1700 ^°C for 15 min leads to the formation of alternating large and small terraces, separated by straight steps of 0.75 nm height on the flat parts of the substrate. A model is proposed which ascribes this bimodal terrace size distribution to the atomic structure of the SiC steps and to H diffusion on the terraces. For the same etching conditions less significant morphological variations were detected on the curved areas of the surface, where dimple grinding had been performed. The beginning of a considerable structural reorganisation of the concave-shaped surfaces was detected only when the etching temperature was increased to 1700 ^°C and the etching time to 1 h. Then, terrace steps with preferential edge orientation along the family of [1120] directions are formed in the concave-shaped areas, as observed by SEM.