Abstract Understanding fossil fuel supply behaviour is crucial for interpreting carbon leakage and assessing the potential effectiveness of border measures in climate policy. In most computable general equilibrium models, this fossil fuel supply is derived from a constant elasticity of substitution production function, in which a natural resource is treated as a fixed factor. We show that this leads to endogenously decreasing supply elasticities and sharply increasing marginal leakage rates for large coalitions that have ambitious emissions targets, particularly when fuel exporters participate in the coalition. We propose an alternative production function that has a constant elasticity of fuel supply, which results in more stable leakage rates and a different share of trade-related leakage. The role of this model variation for the assessment of border measures in climate policy turns out to be limited. In those cases where the model versions differ most (i.e. large coalition, ambitious targets), border measures have a small effect anyway.