In my previous talk, I constructed a model structure on the category of "distinguished Gray-categories" (that is, categories enriched over the cartesian closed category of algebraically cofibrant 2-categories). In this pair of talks, I will define a subcategory of "algebraically cofibrant" distinguished Gray-categories and construct a model structure thereon. I will show that the full subcategory of fibrant objects in this model category is the Cauchy completion of the category of Bicat-enriched categories and "computadic" normal pseudofunctors (a la Garner). In sequels to this talk, I hope to give another description of this full subcategory of fibrant objects in terms of tricategories and to prove that this model category is cartesian closed (all the better to enrich over).