This paper presents a model-independent algorithm for tomography of the ionosphere. Prior knowledge consists of the following pieces of information: electron density cannot be negative, the ionosphere is basically smooth and stratified, and electron density is low at high (≳700 km) and low (≲100 km) altitudes. Tests based on simulated measurements show that the method recovers the latitudinal structure well, whereas the vertical structure is recovered with moderate success: the estimated height of the layer of maximum electron density may be as much as 90 km in error. Because of the imposed smoothness the method tends to underestimate the peak in electron density by as much as one third in unfavorable cases. ¿ 1998 American Geophysical Union