Achieving climate neutrality will require clean alternatives to entirely replace fossil energy carriers and technologies in most economic sectors. However, standard computable general equilibrium (CGE) frameworks, which are widely used to analyse climate policies and rely on nested constant elasticity of substitution (CES) functions, are not well suited for simulating the full substitution of incumbent factor inputs implicit in deep decarbonisation scenarios. This study presents an alternative modelling procedure, based on the logistic distribution, to overcome the "stickiness" of technological diffusion under CES functional forms. Deep decarbonisation scenarios are simulated with a large-scale recursive-dynamic international CGE model to illustrate the advantages of the suggested approach. By decomposing the overall effects of changing functional forms into distinct components, we highlight the way in which key modelling assumptions affect various macroeconomic and climate policy variables.