  Little Higgs models often feature spontaneously broken extra global
symmetries, which must also be explicitly broken in order to avoid massless
Goldstone modes in the spectrum. We show that a possible conflict with
collective symmetry breaking then implies light modes coupled to the Higgs
boson, leading to interesting phenomenology. Moreover, spontaneous CP violation
is quite generic in such cases, as the explicit breaking may be used to
stabilize physical CP odd phases in the vacuum. We demonstrate this in an SU(2)
\times SU(2) \times U(1) variant of the Littlest Higgs, as well as in an
original SU(6)/SO(6) model. We show that even a very small explicit breaking
may lead to large phases, resulting in new sources of CP violation in this
class of models.
