  We study in a systematic way a generic nonderivative (massive) deformation of
general relativity using the Hamiltonian formalism. The number of propagating
degrees of freedom is analyzed in a nonperturbative and background independent
way. We show that the condition of having only five propagating degrees of
freedom can be cast in a set of differential equations for the deforming
potential. Though the conditions are rather restrictive, many solutions can be
found.
