Can one classify finite Postnikov pieces?

The classical approach of constructing finite Postnikov systems by k-invariants is compared with the global approach of Dwyer, Kan, and Smith. We concentrate on the case of 3-stage Postnikov pieces and provide examples where a classification is feasible. In general though, the computational difficulty of the global approach is equivalent to that of the classical one. …all mathematics leads, doesn’t it, sooner or later, to some kind of human suffering. ‘Against the Day’, Thomas Pynchon