  We consider asymptotically anti-de Sitter gravity coupled to tachyonic scalar
fields with mass at or slightly above the Breitenlohner-Freedman bound in d
greater than or equal to 4 spacetime dimensions. The boundary conditions in
these ``designer gravity'' theories are defined in terms of an arbitrary
function W. We give a general argument that the Hamiltonian generators of
asymptotic symmetries for such systems will be finite, and proceed to construct
these generators using the covariant phase space method. The direct calculation
confirms that the generators are finite and shows that they take the form of
the pure gravity result plus additional contributions from the scalar fields.
By comparing the generators to the spinor charge, we derive a lower bound on
the gravitational energy when i) W has a global minimum, ii) the
Breitenlohner-Freedman bound is not saturated, and iii) the scalar potential V
admits a certain type of "superpotential."
