Higher-order corrections (HOC) to Soffer's inequality between the vari
ous parton distributions are determined within the QCD parton model. T
he resulting inequality gives an upper bound to the transversity distr
ibutions determined in the (M) over bar (S) over bar scheme; this boun
d may be used in any process where transversity distributions enter. F
or the u- and d-quarks, the HOC are negative and moderate in magnitude
. For the sea quarks, the HOC are somewhat larger and also negative.