After recalling a definition of a black hole "hair" we explain why the only interesting hairs are those that are also remnants. Next, we will examine a recent proposal by Hawking, Perry and Strominger, who suggest that soft photons and soft gravitons can be regarded as black hole hairs that may be relevant to the black hole information paradox. We will make use of factorization theorems for infrared divergences of the S-matrix to argue that, by appropriately dressing in and out hard states, the soft-quanta-dependent part of the S-matrix becomes essentially trivial, in the sense that the information paradox can be fully formulated in terms of dressed hard states, which do not depend on soft quanta.