  We investigate the electroweak phase transition in the real-singlet extension
of the Standard Model at two-loop level, building upon existing one-loop
studies. We calculate the effective potential in the high-temperature
approximation and detail the required resummations at two-loop order. In
typical strong-transition scenarios, we find deviations of order $20\% - 50\%$
from one-loop results in transition strength and critical temperature for both
one- and two-step phase transitions. For extremely strong transitions, the
discrepancy with one-loop predictions is even larger, presumably due to sizable
scalar couplings in the tree-level potential. Along the way, we obtain a
dimensionally-reduced effective theory applicable for non-perturbative lattice
studies of the model.
