In a recent paper, Anderssen and Davies [Simple moving-average formulae for direct recovery of the relaxation spectrum, Mathematics Research Report MRR 016-98, Centre for Mathematics and its Applications, The Australian National University] have derived moving-average formulae which can be applied to oscillatory shear data to recover estimates of the relaxation spectrum of the viscoelastic material tested. These moving-average formulae represent an improvement over commercial packages currently available, for two reasons. First, they take the limits imposed by sampling localization in determining the relaxation spectrum fully into account. Secondly, to within finite resolution, these formulae yield accurate relaxation spectra in a fraction of a second on a PC. Anderssen and Davies have also indicated that their formulae are best employed within an iterative algorithm which exploits the natural duality between storage and loss moduli. The purpose of this paper is to pursue this natural duality further, and present a class of fast algorithm accessible to the experimentalist. Their performance when applied to noisy data is described. Their success is attributed to the implicit duality constraints imposed through sampling localization and the Kramers-Kronig relations, and to the nature of the regularization imposed.