  Discrete breathers are time-periodic, spatially localized solutions of the
equations of motion for a system of classical degrees of freedom interacting on
a lattice. An important issue, not only from a theoretical point of view but
also for their experimental detection, are their energy properties. We
considerably enlarge the scenario of possible energy properties presented by
Flach, Kladko, and MacKay [Phys. Rev. Lett. 78, 1207 (1997)]. Breather energies
have a positive lower bound if the lattice dimension is greater than or equal
to a certain critical value d_c. We show that d_c can generically be greater
than two for a large class of Hamiltonian systems. Furthermore, examples are
provided for systems where discrete breathers exist but do not emerge from the
bifurcation of a band edge plane wave. Some of these systems support breathers
of arbitrarily low energy in any spatial dimension.
