The study of matrices with a displacement structure is mainly concerned with recursions for the so-called generator matrices. The recursion usually involves free parameters, which can be chosen in several ways so as to simplify the resulting algorithm. In this correspondence we present a choice for the parameters that is motivated by a maximum-entropy formulation, This choice further motivates the introduction of the so-called generalized reflection coefficients which are, in general, different from the better known Schur coefficients.