Models of rail travel demand take one of three generic functional forms: the generalised cost (GC) function where price and the various time variables are combined into a composite term through the use of appropriate values of time; the generalised journey time and fare (GJT-Fare) approach, where the time-related variables are combined into a single term and fare remains separate; and the specification of separate elasticities for all terms, termed the separate components (SC) approach. This research extends that reported by Wardman and Toner (Transportation 47:75–108, 10.1007/s11116-017-9850-7, 2020) in exploring more flexible functional forms where appropriate parameterisation of the standard GC, GJT and SC models allows them to have more general elasticity properties. Whilst the aforementioned study discounted the standard GC approach on the grounds of inferior fit and undesirable elasticity properties, the analysis reported here, based on large datasets, finds best-fitting more flexible models to have elasticity properties that resemble those of the GC approach. Indeed, the preferred functions can deliver elasticities that are somewhat different from those of the GJT-Fare approach that has long provided the basis of official rail demand forecasts in Great Britain. In addition, the study adds to the existing evidence base by providing credible and precise elasticities for GJT and fare, and importantly for the rarely estimated GC and SC elasticities, reaffirms the need of GC models to directly estimate demand consistent values of time, and indicates that the weights currently attached to headway and interchange in formulating GJT are in need of significant amendment. Although the context is rail in Great Britain, the results have relevance to demand analysis of other modes and in other countries as well as to other transport modelling approaches.