I compare two holographic mechanisms giving to the graviton a parametrically-small supersymmetric mass m$_{g}$ in Anti-de Sitter spacetime. In the context of bimetric gravity these mechanisms couple ‘weakly’ two initially decoupled superconformal theories by: (i) turning on a double-trace deformation, or (ii) gauging a common global symmetry. Superconformal invariance restricts the number of Poincaré supercharges to N$_{Q}$ ≤ 4 for mechanism (i) and to N$_{Q}$ ≤ 8 for mechanism (ii), and the AdS dimension to D ≤ 5. The putative effective supergravities are expected to break down in the m$_{g}$ → 0 limit at an intermediate scale between m$_{g}$ and m$_{Planck}$. In a recently-proposed microscopic embedding of mechanism (ii) in string theory [7, 8], I show that m$_{g}$ = 0 is at infinite distance in moduli space, and I relate the breakdown of the effective theory to the condensation of unprotected spin-2 excitations in the string-theoretic description of the ‘holographic bridge’. The phenomenon is invisible in the weakly-coupled CFT side. I conjecture that similar phenomena should be at work in all cases.