  In deep-inelastic scattering experiments, there is a general connection
between subtractions in dispersion relations, violations of sum-rules and
$\delta$-functions in parton distribution functions. It is explained why one
might expect a small violation in sum rules for the twist-3 distribution
functions $g_T(x)$ and $h_L(x)$ when the sum-rules are applied to $x\neq 0$
data only. The non-perturbative predictions are studied in the context of a
one-loop model.
