  Recently, the class of energy-conserving Runge-Kutta methods named
Hamiltonian Boundary Value Methods (HBVMs), has been proposed for the efficient
solution of Hamiltonian problems, as well as for other types of conservative
problems. In this paper, we report further advances concerning such methods,
resulting in their enhanced version (Enhanced HBVMs, or EHBVMs). The basic
theoretical results are sketched, along with a few numerical tests on a
Hamiltonian problem, taken from the literature, possessing multiple invariants.
