  We define compatibility between Jacobi structures and pseudo-Riemannian
cometrics on Jacobi algebroids. This notion is a generalization of the
compatibility between Poisson structures and pseudo-Riemannian cometrics on
manifolds, which was defined by Boucetta. We show that the compatibility with a
cometric is ``preserved'' by the Poissonization of a Jacobi structure.
Furthermore, we prove that for a contact pseudo-metric structure on a manifold,
satisfying the compatibility condition is equivalent to being a Sasakian
pseudo-metric structure.
