  The electroweak symmetry breaking transition may supply the appropriate
out-of-equilibrium conditions for baryogenesis if it is triggered sufficiently
fast. This can happen at the end of low-scale inflation, prompting baryogenesis
to occur during tachyonic preheating of the Universe, when the potential energy
of the inflaton is transfered into Standard Model particles. With the proper
amount of CP-violation present, the observed baryon number asymmetry can be
reproduced. Within this framework of Cold Electroweak Baryogenesis, we study
the dependence of the generated baryon asymmetry on the speed of the quenching
transition. We find that there is a separation between ``fast'' and ``slow''
quenches, which can be used to put bounds on the allowed Higgs-inflaton
coupling. We also clarify the strong Higgs mass dependence of the asymmetry
reported in a companion paper (hep-ph/0604263).
