Achieving ambitious climate change mitigation targets clearly requires a focus on transport that should include changes in travel behaviour in addition to increased vehicle efficiency and low-carbon fuels. Most available energy/economy/environment/engineering (E4) modelling tools focus however on technology and fuel switching and tend to poorly incorporate mitigation options from travel behaviour, and in particular, switching between modes is not an option. This paper describes a novel methodology for incorporating competition between private cars, buses and trains in a least-cost linear optimisation E4 model, called TIMES. This is achieved by imposing a constraint on overall travel time in the system, which represents the empirically observed fixed travel time budget (TUB) of individuals, and introducing a cost for infrastructural investments (travel time investment, TT), which reduces the travel time of public transport. Two case studies from California and Ireland are developed using a simple TIMES model, and results are generated to 2030 for a reference scenario, an investments scenario and a CO2 emissions reduction scenario. The results show that with no travel time constraint, the model chooses public transport exclusively. With a travel time constraint, mode choice is determined by income and investment cost assumptions, and the level of CO2 constraint, with greater levels of public transport in the mitigation scenario. At low travel investment cost, new rail is introduced for short distances and increased bus capacity for longer distances. At higher investment costs rail is increasingly chosen for long distances also. (C) 2014 Elsevier Ltd. All rights reserved.