Value hierarchies structure people's position on specific issues when values are in conflict. This general proposition is tested using surveys of Israeli public opinion on issues relating to the Israeli-Arab conflict. Value priorities are shown to be politically and ideologically structured, and not random, with certain value combinations more prevalent and more enduring than others. Most importantly, we establish that people's value hierarchies significantly structure policy preferences and changes therein. The more salient or acute the value conflict, the greater the correspondence between hierarchy and preference. This value trade-off approach presents a picture of Israeli public opinion which is very different from that usually portrayed: of a population firmly supporting a Jewish majority in their state, with a very strong desire for peace. The values of land and democracy are shown to be much less important.