Periodic solutions of the chemostat model are studied under integral constraints on the washout rate, aiming at improving average water quality. For the one-species chemostat, an optimal control, which may admit a singular arc, is synthesized for convex-concave growth functions. The optimal trajectories generalize the existing ones for convex and concave growth functions. Then, unicity of periodic positive solutions is considered. In the two-species chemostat, a non-generic counterexample where infinitely many positive periodic solutions exist is constructed. In the one-species gradostat, unicity is proven for a rather broad class of configurations. Contrary to many existing results, this result applies for any monotonic growth function.