  We consider the problem of collapse of a self-gravitating Higgs field, with
potential bounded below by a (possibly negative) constant. The behaviour at
infinity may be either asymptotically flat or asymptotically AdS. This problem
has received much attention as a source for possible violations of weak cosmic
censorship in string theory. In this paper, we prove under spherical symmetry
that ``first singularities'' arising in the non-trapped region must necessarily
emanate from the centre. In particular, this excludes the formation of a
certain type of naked singularity which was recently conjectured to occur.
