  The gravitational collapse of a complex scalar field in the harmonic map is
modeled in spherical symmetry. Previous work has shown that a change of
stability of the attracting critical solution occurs in parameter space from
the discretely self-similarity critical (DSS) solution originally found by
Choptuik to the continuously self-similar (CSS) solution found by Hirschmann
and Eardley. In the region of parameter space in which the DSS is the
attractor, a family of initial data is found which finds the CSS as its
critical solution despite the fact that it has more than one unstable mode. An
explanation of this is proposed in analogy to families that find the DSS in the
region where the CSS is the attractor.
