Control of exhaust gas recirculation (EGR) and variable geometry turbine in diesel engines is a challenging problem and model predictive control (MPC) seems to be a promising method. In MPC the choice of output variables, and thereby the criterion, has a direct impact on the optimization problem to solve and the resulting control performance. Different selections of outputs are investigated and discussed, proposing that it is beneficial to include EGR-fraction and pumping losses in the criterion while having the oxygen/fuel ratio as a constraint. The rational for this constraint is that, in diesel engines, it is allowed to have the oxygen/fuel ratio larger than a set-point. The proposed design also includes integral action of the EGR-fraction to handle model errors and prediction of engine load and speed. A comparison is made between the proposed MPC, a proportional-integral-derivative (PID) controller, and an MPC with intake manifold pressure and compressor flow as outputs, which is the common choice in the literature. Comparisons are performed in simulation on the European transient cycle showing the following two points. First, the proposed design gives 9% lower oxygen/fuel ratio error, 80% lower EGR-error, and 12% lower pumping losses compared to an MPC design with intake manifold pressure and compressor flow as outputs. Second, the proposed design gives 9% lower EGR-error and 6% lower pumping losses compared to a control structure with PID controllers with oxygen/fuel ratio and EGR-fraction as the main outputs.