How to choose modified moments?

Modified moments of a nonnegative measure determine uniquely the recurrence coefficients of the polynomials orthogonal with respect to the given nonnegative measure. The sensitivity of the underlying nonlinear maps with regard to perturbations in the modified moments has been studied by Gautschi and Fischer, and is further analyzed in this paper. In particular, we discuss the question of how (not) to choose the support of the underlying two measures.