The purpose of this study is to calculate Pareto surfaces in multi-criteria radiation treatment planning and to analyse the dependency of the Pareto surfaces on the objective functions used for the volumes of interest. We develop a linear approach that allows us to calculate truly Pareto optimal treatment plans, and we apply it to explore the tradeoff between tumour dose homogeneity and critical structure sparing. We show that for two phantom and two clinical cases, a smooth (as opposed to kinked) Pareto tradeoff curve exists. We find that in the paraspinal cases the Pareto surface is invariant to the response function used on the spinal cord: whether the mean cord dose or the maximum cord dose is used, the Pareto plan database is similar. This is not true for the lung studies, where the choice of objective function on the healthy lung tissue influences the resulting Pareto surface greatly. We conclude that in the special case when the tumour wraps around the organ at risk, e.g. prostate cases and paraspinal cases, the Pareto surface will be largely invariant to the objective function used to model the organ at risk.