  For supersymmetric heterotic string compactifications on a Calabi-Yau
threefold $X$ endowed with a vector bundle $V$ the world-sheet superpotential
$W$ is a sum of contributions from isolated rational curves $\C$ in $X$; the
individual contribution is given by an exponential in the K\"ahler class of the
curve times a prefactor given essentially by the Pfaffian which depends on the
moduli of $V$ and the complex structure moduli of $X$. Solutions of $DW=0$ (or
even of $DW=W=0$) can arise either by nontrivial cancellations between the
individual terms in the summation over all contributing curves or because each
of these terms is zero already individually. Concerning the latter case
conditions on the moduli making a single Pfaffian vanish (for special moduli
values) have been investigated. However, even if corresponding moduli -
fulfilling these constraints - for the individual contribution of one curve are
known it is not at all clear whether {\em one} choice of moduli exists which
fulfills the corresponding constraints {\em for all contributing curves
simultaneously}. Clearly this will in general happen only if the conditions on
the 'individual zeroes' had already a conceptual origin which allows them to
fit together consistently. We show that this happens for a class of cases. In
the special case of spectral cover bundles we show that a relevant solution set
has an interesting location in moduli space and is related to transitions which
change the generation number.
