Lebanon's peace deal has cast new light on the prominent role sought by Qatar, a tiny energy-rich Gulf country aspiring to take on a larger Mideast regional diplomatic role while also bidding to host an upcoming Olympics. The deal negotiated with the help of Qatar's ruler is just the latest example of small but rich Gulf countries punching above their weight to get recognized,'' said David Butter, Middle East regional director at the London-based Economist Intelligence Unit. Qatar in particular is known across the Middle East for punching in different directions at the same time, which makes its foreign policy one full of contradictions.  It bankrolls the region's most-watched satellite TV station, Al Jazeera, at odds with most Mideast governments. It also hosts the U.S. military's Central Command, which oversees American operations in Iraq and Afghanistan.