We associate Hanf numbers to triples where T and T1 are theories and p is a type. We show that the Hanf number for the property: “there is a model M1 of which omits p, but is saturated” is larger than the Hanf number of but smaller than the Hanf number of when T is stable with. In fact, surprisingly, we even characterise the Hanf number of when we fix where T is a first order complete (and stable), and demand.