  For a cosmological first-order electroweak phase transition, requiring no
sphaleron washout of baryon number violating processes leads to a lower bound
on the strength of the transition. The velocity of the boundary between the
phases, the so-called bubble wall, can become ultra-relativistic if the
friction due to the plasma of particles is not sufficient to retard the wall's
acceleration. This bubble ``runaway'' should not occur if a successful baryon
asymmetry generation due to the transition is required. Using Boedeker-Moore
criterion for bubble wall runaway, within the context of an extension of the
standard model of particle physics with a real gauge-single scalar field, we
show that a non runaway transition requirement puts an upper bound on the
strength of the first-order phase transition.
