We consider the creation of the cosmological baryon asymmetry in the Two Higgs Doublet Model. We imagine a situation where the masses of the five Higgs particles and the two Higgs vevs are constrained by collider experiments, and demonstrate how the requirement of successful baryogenesis can be used to further constrain the remaining 4-dimensional parameter space of the model. We numerically compute the asymmetry within the scenario of Cold Electroweak Baryogenesis, which is particularly straightforward to simulate reliably.