  We consider an extension of the scalar sector of the Standard Model (SM) by
an additional gauge singlet, which mixes with a part of the SM-like Higgs
doublet. Within this model, parameter-space regions exist that can lead to a
strong first-order electro-weak phase transition, a necessary condition for
electro-weak baryogenesis. We discuss how such regions of the parameter space
can be tested using the SM-like Higgs boson's signal strength measurements, as
well as precision observables, such as e.g. the W-boson mass, at current and
future colliders.
