We analyze recent data on a long series of high-spin states in Pb208 with a self-consistent phonon-coupling model for nuclear excitations based on the Skyrme functionals. The model is the renormalized time-blocking approximation which takes the coherent one-particle-one-hole states of the random-phase approximation (RPA) as starting point to develop more complex configurations beyond RPA. To the best of our knowledge, this is the first investigation of high spin states in Pb208 using self-consistent nuclear models. The interesting point here is that complex configurations are compulsory to describe the upper end of the long spin series at all. The data thus provide an ideal testing ground for phonon-coupling models as they give direct access to complex configurations. We find that standard Skyrme functionals which perform well in ground state properties and giant resonance excitations deliver at once an agreeable description of these high spin states.