We consider a conservation law with convex flux, perturbed by a saturating diffusion and non-positive dispersion of the form u(t)+f(u)(x)=epsilon(u(x)root 1+u(x)(2))(x)-delta(|u(xx)|(n))(x). We prove the convergence of the solutions \u(epsilon,delta)\ to the entropy weak solution of the hyperbolic conservation law, u(t)+f(u)(x)=0, for all real number 1 <= n <= 2 provided delta=o(epsilon(n(n+1)/2);epsilon(n+1/n)).