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Measuring Function Points following the standard process is sometimes long and expensive. To solve this problem, several early estimation methods have been proposed. Among these, the “NESMA Estimated” method is one of the most widely used; it has also been selected by the International Function Point User Group as the official early function point analysis method, under the name of ‘High-level FPA’ method. A large-scale empirical study has shown that the High-level FPA method – although sufficiently accurate – tends to underestimate the size of software. Underestimating the size of the software to be developed can easily lead to wrong decisions, which can even result in project failure. In this paper we investigate the reasons why the High-level FPA method tends to underestimate. We also explore how to improve the method to make it more accurate. Finally, we propose size estimation models built using different criteria and we evaluate the estimation accuracy of these new models. Our results show that it is possible to derive size estimation models from historical data using simple regression techniques: these models are slightly less accurate than those delivered by the High-level FPA method in terms of absolute estimation errors, but can be used earlier than the High-level FPA method, are cheaper, and do not underestimate software size.