PAYG (Pay-As-You-Go) transfer schemes may take different forms. In this article I classify those proposed in the literature in three main classes. I present a new variant, labelled ES, or “Equitable and Stable”, and discuss some of its distinctive features, with special regards to its demographic rationale. There are two main innovations in the proposed system: 1) its use of a reference, instead of the current, age structure, with the implication that, in each period, the system may incur deficits, or accumulate assets, that even out in the long run; 2) its use of average incomes of age groups (the young, adults, and the elderly) instead of average incomes of social groups (workers and pensioners). These novelties, combined with the use of relative (as opposed to absolute) incomes, create an original mechanism. Theoretical arguments and computer simulations indicate that ES differs from, and compares favourably with, other versions of PAYG.