Various issues surrounding a recently proposed inequality among twist-
two quark distributions in the nucleon are discussed. We provide a rig
orous derivation of the inequality in QCD, including radiative correct
ions and scale dependence. We also give a more heuristic, but more phy
sical derivation, from which we show that a similar inequality does no
t exist among twist-three quark distributions. We demonstrate that the
inequality does not constrain the nucleon's tensor charge. Finally we
explore physical mechanisms for saturating the inequality, arguing it
is unlikely to occur in nature.