Next-to-leading order (NLO) effects oil Soffer's transversity bound are stu
died. It is shown that defining the NLO corrections to the transversity via
Drell-Yan lepton-pair production, I,ut to the unpolarized and longitudinal
ly polarized distributions via deep inelastic scattering. results in a subs
tantial suppression of the bound for all q = u, d and sea. Moreover assumin
g that the bound is saturated at Q(o)(2) = 4 GeV2 and evolving the NLO dist
ributions to Q(2) > Q(o)(2) via 2-loop split functions, it is shown that th
e bound is not violated.