In recent years, several nonparametric robust identification algorithms have been proposed that generate a collection of frequency-dependent value sets where the "true" model of an linear time-invariant system is assumed to lie. If the system is also assumed to have restricted complexity, then the identified value sets mag be conservative. The purpose of this paper is to investigate this problem of conservativeness from a set membership viewpoint and propose an algorithm for computing the largest value sets contained in the original ones that can be generated by a model of fixed structure but unknown parameters.