  It is shown that a large class of weak disturbances on macroscopic quantum
superpositions can be canceled by a probabilistic reversing operation on the
system. We illustrate this for spin systems undergoing an Ising-type
interaction with the environment and demonstrate that both the fidelity to the
original state and the purity of the amended state can simultaneously be
increased by the reversing operation. A possible experimental scheme to
implement our scheme is discussed.
