Perturbative inversion techniques are extended to finite-shell model spaces. The parameters in a Hamiltonian are determined from a set of eigenvalues, by iterating a perturbative technique in which the matrix equivalent of a Fredholm kernel is inverted. Tests applied to realistic nuclear systems show that the method is rapidly convergent and stable, and especially useful in cases where an effective Hamiltonian has to be fine-tuned to describe a special group of states.