  We say that a projective class in a triangulated category with coproducts is
perfect if the corresponding ideal is closed under coproducts of maps. We study
perfect projective classes and the associated phantom and cellular towers.
Given a perfect generating projective class, we show that every object is
isomorphic to the homotopy colimit of a cellular tower associated to that
object. Using this result and the Neeman's Freyd--style representability
theorem we give a new proof of Brown Representability Theorem.
