  The effective potential obtained by loop expansion is usually not real in the
range of field values explored by its minima during a phase transition. We
apply the optimized perturbation theory in a fixed gauge to singlet scalar
extensions of the Standard Model in order to calculate a one-loop effective
potential that is real by construction. We test this computational scheme by
comparing such a potential obtained in Landau gauge to that derived based on
the Higgs pole mass. We carry out the latter construction by imposing physical
renormalization conditions, which yields a potential without residual
regularization scale dependence. We use our effective potential to study the
parameter dependence of the critical temperatures in a two-step phase
transition of the form $(0,0)\to (0,w')\to (v,w)$ that occurs for decreasing
temperature in scalar extensions of the SM with two vacuum expectation values
$v$ and $w$.
