A new procedure is described for the calculation of real height profiles from ionospheric h′(ƒ) records. The equations are formulated in a way which can reproduce all current methods of analysis, and provide many powerful extensions. For general use a sixth-order overlapping polynomial analysis is recommended, with real height sections determined by a least squares fit to real and virtual height data. Coefficients can also be obtained for single polynomials fitted separately to each ionospheric layer. All methods include Chapman layer peaks, and a model valley between layers. High-order least squares calculations give greater accuracy and stability than any current procedures, and are particularly suitable for the analysis of high-density data from digital ionosondes.