  It is widely believed that the existence of singlet scalars in some Standard
Model extensions can easily make the electroweak phase transition strongly
first order, which is needed for the electroweak baryogenesis scenario. In this
paper, we will examine the strength of the electroweak phase transition in the
simplest extension of the Standard Model with a real singlet using the
sphaleron energy at the critical temperature. We find that the phase transition
is stronger by adding a singlet; and also that the criterion for a strong phase
transition Omega (Tc)/Tc>1, where Omega =(v^2+(x-x0)^2)^(1/2) and x (x0) is the
singlet vev in the broken (symmetric) phase, is not valid for models containing
singlets, even though often used in the literature. The usual condition vc/Tc>1
is more meaningful, and it is satisfied for a large part of the parameter space
for physically allowed Higgs masses.
