As the modern world is facing economic limits and an increase in ecological and social problems, the need for innovative and sustainable solutions becomes more pressing. This has consequences for the investment market, where the integration of sustainability-related objectives becomes an important development. Yet investment theory and especially modern portfolio theory does not allow the consideration of other criteria than return and risk. In this paper, a method is proposed that enhances Markowitz' modern portfolio theory and allows the investor to define a flexible degree of sustainability as an additional optimisation-criterion in the portfolio selection process. The method is applied to the investment universe of the German stock-index DAX and analysed empirically over the period 2003-2010. The observed effects are compared both in terms of achieved performance and the degree of sustainability with the DAX as a benchmark. The results show that the three-dimensional optimisation as a possible synthesis of portfolio theory and sustainable investment can achieve good results with respect to both financial and sustainability objectives, and that it forms a good starting basis for a further and more detailed elaboration.