  A Redheffer type description of the set of all contractive solutions to the
relaxed commutant lifting problem is given. The description involves a set of
Schur class functions which is obtained by combining the method of isometric
coupling with results on isometric realizations. For a number of special cases,
including the case of the classical commutant lifting theorem, the description
yields a proper parameterization of the set of all contractive solutions, but
examples show that, in general, the Schur class function determining the
contractive lifting does not have to be unique. Also some sufficient conditions
are given guaranteeing that the corresponding relaxed commutant lifting problem
has only one solution.
