  We consider an extension of the results of S. Bando, R. Kobyashi, G. Tian,
and S. T. Yau on the existence of Ricci-flat K\"{a}hler metrics on
quasi-projective varieties Y=X\D with \alpha[D]=c_1(X), \alpha >1. The
requirement that D admit a K\"{a}hler-Einstein metric is generalized to the
condition that the link S in the normal bundle of D admits a Sasaki-Einstein
structure in the Sasaki-cone of the usual Sasaki structure provided the
embedding D\subset X satisfies an additional holomorphic condition. If D is a
toric variety, then S always admits a Sasaki-Einstein metric. As an application
we prove that every small smooth deformation of a toric Gorenstein singularity
admits a complete Ricci-flat K\"{a}hler metric asymptotic to a Calabi ansatz
metric. Some examples are given which were not previously known.
