  We analyze recent data on a long series of high-spin states in $^{208}$Pb
with a self-consistent phonon-coupling model for nuclear excitations based on
the Skyrme functionals. The model is the renormalized time-blocking
approximation (RenTBA) which takes the coherent one-particle-one-hole (1p1h)
states of the random-phase approximation (RPA) as starting point and develops
from that more complex configurations beyond RPA. To the best of our knowledge,
this is the first investigation of high spin states in $^{208}$Pb 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.
