  The paper deals with perturbations of the equation that have a number of
conservation laws. When a small term is added to the equation its conserved
quantities usually decay at individual rates, a phenomenon known as a selective
decay. These rates are described by the simple law using the conservation laws'
generating functions and the added term. Yet some perturbation may retain a
specific quantity(s), such as energy, momentum and other physically important
characteristics of solutions. We introduce a procedure for finding such
perturbations and demonstrate it by examples including the KdV-Burgers equation
and a system from magnetodynamics. Some interesting properties of solutions of
such perturbed equations are revealed and discussed.
