<p>There are two dominant criteria for evaluating social welfare, the utilitarian and maximin criteria. Both exhibit extreme properties: the utilitarian criterion focuses exclusively on efficiency, while the maximin criterion is highly concerned with the utility level of the least advantaged individuals. To consider more moderate criteria, this paper modifies the axioms postulating their extreme attitudes. More specifically, we relax Hammond equity of the maximin criterion and the additivity property of the utilitarian criterion. We show that together with standard axioms, these modified axioms characterize the convex combinations of these two welfare criteria, which we call the mixed utilitarian-maximin social welfare orderings.</p>