  Perturbative probability conservation provides a strong constraint on the
presence of new interactions of the Higgs boson. In this work we consider CP
violating Higgs interactions in conjunction with unitarity constraints in the
gauge-Higgs and fermion-Higgs sectors. Injecting signal strength measurements
of the recently discovered Higgs boson allows us to make concrete and
correlated predictions of how CP-violation in the Higgs sector can be directly
constrained through collider searches for either characteristic new states or
tell-tale enhancements in multi-Higgs processes.
