  It is well known that the solutions of a (relaxed) commutant lifting problem
can be described via a linear fractional representation of the Redheffer type.
The coefficients of such Redheffer representations are analytic operator-valued
functions defined on the unit disc D of the complex plane. In this paper we
consider the converse question. Given a Redheffer representation, necessary and
sufficient conditions on the coefficients are obtained guaranteeing the
representation to appear in the description of the solutions to some relaxed
commutant lifting problem. In addition, a result concerning a form of
non-uniqueness appearing in the Redheffer representations under consideration
and an harmonic maximal principle, generalizing a result of A. Biswas, are
proved. The latter two results can be stated both on the relaxed commutant
lifting as well as on on the Redheffer representation level.
