  For an arbitrary smooth n-dimensional Fano variety $X$ we introduce the
notion of a small toric degeneration. Using small toric degenerations of Fano
n-folds $X$, we propose a general method for constructing mirrors of Calabi-Yau
complete intersections in $X$. Our mirror construction is based on a
generalized monomial-divisor mirror correspondence which can be used for
computing Gromov-Witten invariants of rational curves via specializations of
GKZ-hypergeometric series.
