  We define Q-normal lattice polytopes. Natural examples of such polytopes are
Cayley sums of strictly combinatorially equivalent lattice polytopes, which
correspond to particularly nice toric fibrations, namely toric projective
bundles. In a recent paper Batyrev and Nill have suggested that there should be
a bound, N(d), such that every lattice polytope of degree d and dimension at
least N(d) decomposes as a Cayley sum. We give a sharp answer to this question
for smooth Q-normal polytopes. We show that any smooth Q-normal lattice
polytope P of dimension n and degree d is a Cayley sum of strictly
combinatorially equivalent polytopes if n is greater than or equal to 2d+1. The
proof relies on the study of the nef value morphism associated to the
corresponding toric embedding.
