  Sum rules for twist-3 distributions are reexamined. Integral relations
between twist-3 and twist-2 parton distributions suggest the possibility for a
$\delta$-function at $x=0$. We confirm and clarify this result by constructing
$h_L$ and $h_L^3$ (quark-gluon interaction dependent part of $h_L$) explicitly
from their moments for a one-loop dressed massive quark. The physics of these
results is illustrated by calculating $h_L(x,Q^2)$ using light-front
time-ordered pQCD to ${\cal O}(\alpha_S)$ on a quark target. A $\delta(x)$ term
is also found in $e(x,Q^2)$, but not in $g_T(x,Q^2)$, to this order in ${\cal
O}(\alpha_S)$.
