The theory of optimal output feedback control is extended to a class of quadratic performance measures whose weighting matrices are functions of frequency. The incorporation of frequency-dependent weighting matrices allows one to emphasise or de-emphasise the importance of the variables being penalised over specific bands of frequencies. Optimization of the frequency-shaped performance measure yields optimal compensators that can be more meaningful for certain minimisation problems. Results are presented for different configurations of frequency-shaping feedback control. An example is presented to illustrate the usefulness of the design technique.