  We evaluate the maximal Bell violation for a generic qubit-qudit system,
obtaining easily computable expressions in arbitrary qudit dimension. This work
generalizes the well-known Horodeckis's result for a qubit-qubit system. We
also give simple lower and upper bounds on that violation and study the
possibility of improving the amount of Bell-violation by embedding the qudit
Hilbert space in one of larger dimension. The results are illustrated with a
family of density matrices in the context of a qubit-qutrit system.
