In a recent paper (Beghi, Lepschy & Viaro (1997) IEEE Transactions on Circuits and System-I, 44, 824-828) a procedure for obtaining proper rational approximants of the transfer function of a delay was suggested. We study a generalization of the feedback problem posed in the cited paper and obtain its general solution. Explicit computations of the generalized approximants are obtained in terms of Bernoulli numbers and it is found that they correspond to iterate resummations of the approximants in (Beghi et al., 1997) before truncation. The properties and frequency performance of the new rational approximants are studied and compared to those of the original ones.