  We discuss the question if the upcoming generation of collider and low-energy
experiments can successfully probe the nature of the electroweak phase
transition. In particular, we are interested in phase transitions strong enough
for electroweak baryogenesis or even for a production of gravitational
radiation observable by the Big Bang Observer.
  As an explicit example, we present an analysis in a singlet extension of the
Standard Model. We focus on the region in parameter space where the model
develops no significant deviation in its low energy phenomenology from the
Standard Model. Nevertheless, this class of models can develop a very strong
phase transition.
