  We reexamine the estimate of the neutron Electric Dipole Moment (NEDM) from
chiral and QCD spectral sum rules (QSSR) approaches. In the former, we evaluate
the pion mass corrections which are about 5% of the leading Log. results.
However, the chiral estimate can be affected by the unknown value of the
renormalizaton scale nu. For QSSR, we analyze the effect of the nucleon
interpolating currents on the existing predictions. We conclude that previous
QSSR results are not obtained within the optimal choice of these operators,
which lead to an overestimate of these results by about a factor 4. The weakest
upper bound |theta|< 2 10^-9 for the strong CP-violating angle is obtained from
QSSR, while the strongest upper bound |theta|< 1.3 10^-10 comes from the chiral
approach evaluated at the scale \nu=M_N. We also re-estimate the proton
magnetic susceptibility, which is an important input in the QSSR estimate of
the NEDM.
