  Vacuum compactifications may suffer from instabilities under small
perturbations or tunnel effects; both are difficult to analyze. In this paper
we consider the issue from a higher-dimensional perspective. We first look at
how stability works for supersymmetric vacua, where it is widely expected to
hold. We first show that the nucleation of brane bubbles in type II AdS
compactifications is forbidden in the probe approximation by a simple argument
involving pure spinors and calibrations. We then adapt familiar positive-energy
theorems directly to M-theory and type II supergravity, rather than to their
effective lower-dimensional reductions, also showing how to consistently
include localised sources. We finally initiate an analysis of how these
arguments might be extended to non-supersymmetric vacua. In M-theory, at the
lower-derivative level, we find that the most natural modifications fail to
stabilize the skew-whiffed and Englert vacua.
