  We re-examine the estimates of the higher twist contributions to the integral
of $g_1$, the polarised structure function of the nucleon, based on QCD sum
rules. By including corrections both to the perturbative contribution and to
the low energy contribution we find that the matrix elements of the relevant
operators are more stable to variations of the Borel parameter $M^2$, allowing
for a meaningful estimate of the matrix elements. We find that these matrix
elements are typically twice as large as previous estimates. However, inserting
these new estimates into the recently corrected expressions for the first
moments of $g_1$ leads to corrections too small to affect the phenomenological
analysis. For the unpolarised case the higher twist corrections to the GLS and
Bjorken sum rules are substantial and bring the estimate of $\Lambda_{QCD}$
from the former into good agreement with that obtained from the $Q^2$
dependence of deep inelastic data.
