We construct on ℝ2d, for any d ≥ 3, smooth Hamiltonians having an elliptic equilibrium with an arbitrary frequency, that is not accumulated by a positive measure set of invariant tori. For d ≥ 4, the Hamiltonians we construct have not any invariant torus of dimension d. Our examples are obtained by a version of the successive conjugation scheme à la Anosov-Katok.