The stochastic inversion method in ionospheric radiotomography is reviewed with a special emphasis on regularization used in the inversion process. Regularization is used both for preventing vigorous point-to-point oscillations and for controlling the peak altitude and thickness of the inversion result. The latter usually means importing a priori information on the layer height and thickness to the solver. In this paper it is pointed out that due to the curvature of the Earth and of the ionosphere, the measurements contain some information on the ionospheric altitude and the profile shape even in the case of a purely horizontally stratified layer. If this information could be used in choosing an appropriate regularization, no additional information would be needed. Simulation tests are presented which indicate that the altitude of a horizontally stratified layer can be determined with a reasonable accuracy without any a priori information. An attempt is also made to use the data for determining the shape of a proper regularization profile. Although some success is achieved in this effort, it is concluded that available a priori information, for example, ionosonde or incoherent scatter measurements, should be used in choosing the regularization profile. The ideas are tested with true data obtained from difference Doppler measurements carried out in Scandinavia, and the results are compared with simultaneous observations made by the European incoherent scatter radar. The comparison shows a reasonable agreement, although clear discrepancies also occur, for instance, in the shape of the bottomside profile.