A direct adaptive control methodology for the rejection of unmeasured non-vanishing disturbances is proposed. The approach uses the framework of polynomial RST controllers and relies on the internal model principle with additional degrees of freedom provided by the Q parametrization. The parameters of the Q polynomial are adapted using minimization of the closed-loop output error. Asymptotic disturbance rejection of unmeasured non-vanishing disturbances can be guaranteed despite plant-model mismatch, provided the closed-loop system remains stable. A simulation example illustrates the theoretical developments.