  Two new sum rules for the quark tensor charges of the nucleon are proposed,
based on a relation connecting the quark transversity distributions to the
quark helicity distributions and the quark model spin distributions, and on the
sum rules for the quark helicity distributions. The two sum rules are useful
for an estimate of the values of the quark tensor charges $\delta U$ and
$\delta D$ from the measured quantities of $\Gamma^p$, $\Gamma^n$, $g_A/g_V$
and $\Delta S$, and two model correction factors with limited uncertainties. We
predict a small value for the sum of the quark tensor charges compared to most
other predictions, in analogy to the unexpectedly small quark helicity sum
which gave rise to the proton ``spin puzzle''.
