Building client/owners need estimates of likely construction costs for budgeting purposes early in the procurement process when little detailed design information is available beyond the type, size and location of the facility. One of the more sophisticated techniques available for this purpose is the storey enclosure method, developed by James in 1954. This uses the basic physical measurements of the building envelope, together with an arbitrary set of multipliers, or weights, to forecast tender/bid prices. Although seldom used in practice, James succeeded in showing his method to be capable of significantly outperforming alternative approaches. The research reported in this paper aimed firstly to reassess James' claims with new data and secondly to advance his method by using regression techniques to obtain the weights involved. Based on data from 138 completed Hong Kong projects for four types of building, two types of regression models were developed. This involved the use of sophisticated features such as leave-one-out cross validation to simulate the way in which forecasts are produced in practice and a dual stepwise selection strategy that enhances the chance of identifying the best model. An algorithm was also designed to select the appropriate parametric and non-parametric tests for objective and rigorous model evaluation against alternatives. The results indicate that, contrary to James' claim, both his original method and the two regression-based alternatives are not significantly better or worse than other models. Surprisingly, the widely used floor area model was found to under-perform in terms of consistency for offices and private housing. For private housing in particular, it was felt that the storey enclosure method was likely to offer good prospects of improvement on those methods currently in use in practice.