We argue the case for a new paradigm for architecting structured P2P overlay networks, coined AESOP. AESOP consists of 3 layers: (i) an architecture, PLANES, that ensures significant performance speedups, assuming knowledge of altruistic peers; (ii) an accounting/auditing layer, AltSeAl, that identifies and validates altruistic peers; and (iii) SeAledPLANES, a layer that facilitates the coordination/collaboration of the previous two components. We briefly present these components along with experimental and analytical data of the promised significant performance gains and the related overhead. In light of these very encouraging results, we put this three-layer architecture paradigm forth as the way to structure the P2P overlay networks of the future.