We argue that the van Dam–Veltman–Zakharov discontinuity arising in the M² → 0 limit of the massive graviton through an explicit Pauli–Fierz mass term could be absent in anti-de Sitter space. This is possible if the graviton can acquire mass spontaneously from the higher-curvature terms and/or the massless limit M² → 0 is attained faster than the cosmological constant Λ → 0. We discuss the effects of higher-curvature couplings and an explicit cosmological term (Λ) on the stability of such a continuity and of massive excitations.