The much debated issue of the transverse single spin asymmetry A_N observed in the inclusive large P_T production of a single hadron in pp interactions, p(transv. polarized) p --> pion X, is considered in a TMD factorization scheme. A previous result [1,2] stating that the maximum contribution of the Collins effect is strongly suppressed, is revisited, correcting a numerical error. New estimates are given, adopting the Collins functions recently extracted from SIDIS and e+e- data, and phenomenological consequences are discussed.