  We discuss what appears the last hope for an astrophysical solution to the
solar neutrino problem: a correlated variation of the astrophysical factors for
the helium burning cross sections ($S_{33}$ and $S_{34}$) and either $S_{17}$
or the central temperature $T_c$. In this context, we recognize the important
role played by the CNO neutrinos. In fact, we can obtain a fair fit to the
experimental data only if three conditions are met simultaneously: the
astrophysical factor $S_{33}$ is about 200 times what is presently estimated,
the astrophysical factor $S_{17}$ is about 3 times larger and the $^{13}$N and
$^{15}$O neutrino fluxes are negligible compared to the ones predicted by
standard solar models. These conditions are not supported by the present data
and their correlated combination is improbable.
