  We develop methods to compute holomorphic Yukawa couplings for heterotic
compactifications on complete intersection Calabi-Yau manifolds, generalising
results of an earlier paper for Calabi-Yau hypersurfaces. Our methods are based
on constructing the required bundle-valued forms explicitly and evaluating the
relevant integrals over the projective ambient space. We also show how our
approach relates to an earlier, algebraic one to calculate the holomorphic
Yukawa couplings. A vanishing theorem, which we prove, implies that certain
Yukawa couplings allowed by low-energy symmetries are zero due to topological
reasons. To illustrate our methods, we calculate Yukawa couplings for
SU(5)-based standard models on a co-dimension two complete intersection
manifold.
