Our study of the so-called generalized regulation problem depends on the classical notions of exact and almost disturbance decoupling. These classical notions are reexamined while considering a very broad category of controllers beyond the classical state and measurement feedback. Such controllers include classical state feedback and measurement feedbacks but also extensions where part of the disturbance signal can be used for feedback. We consider the case where, for a part of the disturbance signal, either all its derivatives up to a certain jth order or derivatives of arbitrary order are available. This is combined with state and with measurement feedback.