In this paper it will be shown how conditional presuppositions can be strengthened to unconditional ones if we assume that the antecedent and consequent of a conditional presupposition are independent of one another. Our notion of independence is very weak, and based on Lewis' (1988) notion of orthogonality of questions. It will be argued that our way of strengthening these presuppositions does not give rise to some wrong predictions Geurts (1996) argued other proposed strengthening accounts do.