  We consider the integer points in a unimodular cone K ordered by a
lexicographic rule defined by a lattice basis. To each integer point x in K we
associate a family of inequalities (lex-cuts) that defines the convex hull of
the integer points in K that are not lexicographically smaller than x. The
family of lex-cuts contains the Chvatal-Gomory cuts, but does not contain and
is not contained in the family of split cuts. This provides a finite cutting
plane method to solve the integer program min{cx : x \in S \cap Z^n }, where S
\subset R^n is a compact set and c \in Z^n . We analyze the number of
iterations of our algorithm.
