  It is known that the underlying spaces of all abelian quotient singularities
which are embeddable as complete intersections of hypersurfaces in an affine
space can be overall resolved by means of projective torus-equivariant crepant
birational morphisms in all dimensions. In the present paper we extend this
result to the entire class of toric l.c.i.-singularities. Our proof makes use
of Nakajima's classification theorem and of some special techniques from toric
and discrete geometry.
