The availability of representative empirical models of the variation of the electron concentration with height in the ionosphere is one critical element in the development of practical schemes for providing reliable HF radio propagation predictions. The degree to which a specific model succeeds must be judged against three criteria: (1) quality of profile match: the model must reproduce the range of N(h) profiles encountered in practice; this match should be maintained in the first and second derivatives with height; (2) availability and simplicity of the external data required for profile specification: input data which consist of only those parameters routinely scaled from ionograms and available from CCIR predictions best fit this criterion; (3) numerical complexity: preferably the mathematical algorithms describing the model should be as simple as possible. These criteria conflict so that schemes have been developed optimized with respect to one or two of them at the expense of the other(s), the choice being driven by the application. In this paper, four such schemes are reviewed and contrasted in the light of these criteria and usage in practice. It is concluded that the Booker (1977) “skeleton” profile approach is best for simulating a known profile for precision radio wave studies, while the Dudeney (1978) technique provides good overall performance for general purpose communications predictions. The performance of the scheme currently recommended by the CCIR (Bradley and Dudeney, 1973a) cannot match these two, and should be superceded except where the need for mathematical simplicity is of overriding importance. The International Reference Ionosphere profile is found to have significant disadvantages for communications work with respect to all three criteria.