Ionospheric tomography uses total electron content (TEC) records collected by longitudinally aligned stations, which receive a beacon satellite orbiting overhead. The electron density distribution is reconstructed for the region bounded by the satellite orbit and the line of ground receivers. A new reconstruction algorithm is described which satisfies the TEC records, makes use of an ionospheric model, and allows the incorporation of complementary measurements. The new algorithm also accepts relative (rather than absolute) TEC as input data. A comparison of the new algorithm and one used recently shows significant improvement over early techniques, particularly when a scaled ionogram is included in the data.