  Let f be an obstructed Thurston map with canonical obstruction \Gamma_f. We
prove the following generalization of Pilgrim's conjecture: if the first-return
map F of a periodic component C of the topological surface obtained from the
sphere by pinching the curves of \Gamma_f is a Thurston map then the canonical
obstruction of F is empty. Using this result, we give a complete topological
characterization of canonical Thurston obstructions.
