  We show that any finite quantum system $S$ can be coupled to a dephasing
environment in such a way that the internal mechanism responsible for
relaxation of observables acting on $S$ can be effectively canceled. By
adjusting this coupling, the difference between the initial and the long--time
expectation values of any observable on $S$ can be tuned to arbitrarily small
however nonzero value. This statement is exemplified and visualized by
numerical studies of relaxation in a generic one-dimensional system of
interacting fermions.
