My prevision of the papacy’s more or less immediate future differs from that of R. H. Benson, the Roman Catholic H. G. Wells, in his two novels Lord of the World and Dawn of All, by being neither eschatological nor ultramontane. To save prognostications about an institution’s future from being mere fiction one should try to control them by some consideration of its past. So I will begin my essay in fortunetelling by a glance at an earlier post-conciliar papacy, and thus try to set up a contrast between the papacy after the two councils of the Vatican and the papacy after the two councils of Constance and Bâsle/Florence in the fifteenth century. It is generally recognised that this episode of Church history is of special relevance to us today. It is discussed by Hans Kung in Structures of the Church), by Paul de Vooght in Les Pouvoirs du Concile et L’Autorité du Pape au Concile de Constance), and by Olivier de la Brosse in Le Pape et le Concile ... àla Veille de la Reforme). Without of course wasting our time by reviving the old papalist-conciliarist controversies of that epoch, we can profitably enquire why in the event they were so sterile, and whether in fact they have ever been satisfactorily resolved, and if not, whether we are today on the threshold of such a resolution.