Would Middle East Peace Perturb Iran?

At the Nixon Center's "National Interest" blog, Paul Pillar joins those who urge President Obama to impose a peace between Israel and the Palestinians. For one thing, there's Iran:

[T]he most important point to make about the peace process and Iran is that an Israeli-Palestinian settlement, far from being a diversion from efforts to contain any dangers from Iran, would instead give a boost to those efforts. Given how much Iranian hardliners exploit politically and diplomatically the Israeli occupation and festering Palestinian problem, a peace settlement would take wind out of this Iranian sail and reduce Iranian appeal and influence in the region.