A variational principle is constructed for gravity coupled to an asymptotically linear dilaton and a p-form field strength. This requires the introduction of appropriate surface terms—also known as 'boundary counterterms'—in the action. The variation of the action with respect to the boundary metric yields a boundary stress tensor, which is used to construct conserved charges that generate the asymptotic symmetries of the theory. In most cases a minimal set of assumptions leads to a unique set of counterterms. However, for certain examples we find families of actions that depend on one or more continuous parameters. We show that the conserved charges and the value of the on-shell action are always independent of these parameters.