This paper deals with the set inversion problem X = f −1 (Y) in the case where f : R n → R m depends on a parameter vector p ∈ R q which is known to be inside a box [p]. We show that for a large class of problems, we can obtain an accurate approximation of the solution set, without bisecting in the p-space. To do this, symbolic methods are required to cast our initial problem into a chain of set-inversion problems, the links of which have some nice properties with respect to p. As an application, we consider the problem of computing the set of all initial states of an uncertain discrete-time state system that reach a target set Y in a given time.