Within certain limitations, this work shows that the production of polymers with any prespecified number average chain length and polydispersity is theoretically feasible when “living” anionic polymerizations are carried out in continuous stirred tank reactors (CSTRs) which are under optimal periodic forcing of the feed flows. The optimal periodic control problem was solved adopting a suboptimal objective function and a novel iterative numerical procedure. When the objective function is minimized in order to reduce the time average polydispersity, then the operation tends to become a sequential semibatch process. Conversely, if the objective is to maximize these variables, then the reagent concentrations inside the reactor tend to be 180° out of phase. Different periods of oscillation must be selected depending on whether the required average polydispersities are above or below the steady state value of 2. The greatest flexibility in the MWD control is obtained with fast kinetics, and, in this case, average polydispersities between 1.06 and 9.2 may be required.