Well-known model predictive control (MPC) theory for constrained linear time-invariant (LTI) systems is extended to accommodate hard constraints and cost penalizations on the spectra of the system’s output trajectories. Thus the proposed method facilitates enforcing constraints, and placing weights, on the harmonic content of input-, state- and output-trajectories, in addition to the usual constrained control objectives. The proposed methods are demonstrated by the example problem of reducing torsional vibrations in a drive-shaft.