THE LATEST SOUNDS of shooting in Lebanon conceal signs of a certain limited but precious progress toward settling down that broken country. What happened was this: The Lebanese government, struggling to reassert its authority, finally cranked itself up to take what is for it the giant step of sending 500 soldiers into the zone patrolled by United Nations peacekeepers in the south. Major Saad Haddad, the Christian militia leader in effect hired by the Israelis to police their border with Lebanon, opened fire. He killed one U.N. soldier and wounded eight others, but the Lebanese troops took up their new positions all the same. Major Haddad then declared the shifting sliver of territory he controls to be the independent state of "Free Lebanon." That got a bit of press play-plus some condemnation in assorted corners of the international community. But the important thing is that the Lebanese government has, however symbolically, asserted new control.

Nor was this the first such assertion by the government of President Elias Sarkis in Beirut. Last month, Saudi Arabia, jittery about developments elsewhere, withdrew its troops from the mostly Syrian "Arab Deterrent Force" put in place in 1976 to help end Lebanon's pitiless civil war. The Saudi units had occupied a key buffer area in Beirut, and their withdrawal raised the possibility of renewed tension or worse between the Syrians and the right-wing Christian militias suspicious of them. Yet there too the Lebanese government successfully moved in its own men. As in the south, the deployment was symbolic since the Lebanese units have little military weight and can be brushed aside at almost any time. But as in the south, the deployment was also more than symbolic: It required assembling units of the two pricipal religious communities in Lebanon and crossing a formidable set of political obstacles to get them in place: good practice for governing.

No one familiar with the tragedy of Lebanon claims to see light at the end of the tunnel. The disputes and rivalries that produced its civil war remain essentially untreated. The Palestinian presence still salts its other wounds. Israel, holding sway in southern Lebanon through the proxy of Major Haddad, hesitates yet to yield either to the United Nations or to the Lebanese government. But the rivalries among Lebanese are, at least for now, subdued. The Syrians are playing the role of peacekeeper as well as empire builder. The Israelis did finally get Major Haddad to stop shooting at the U.N. and they have not recognized his absurd "Free Lebanon." The U.N. peacekeepers, though their ranks rotate, are still in the line. Most encouraging of all, President Sarkis is starting to act the leader.