The mixed sensitivity minimization problem is revisited for a class of single-input-single-output unstable infinite dimensional plants with low order weights. It is shown that H∞ controllers can be computed from the singularity conditions of a parameterized matrix whose dimension is the same as the order of the sensitivity weight. The result is applied to the design of H∞ controllers with integral action. Connections with the so-called Hamiltonian approach are also established.