That could be any time soon. Western military sources believe that the Croats, nominal allies of the Muslims, are for the first time giving significant artillery support to Bosnian troops as they fight to ease the choke hold on the encircled capital. So far, it has been the most successful push by the Muslims to regain territory around Sarajevo in the three-year war with the Serbs. In predawn attacks late last week, the Bosnians pressed on at least five fronts in an effort to turn Serb-held strongholds into vulnerable enclaves. Government forces cut off a key supply route on the road to Pale, the Bosnian Serb capital, and got close enough to fire on the town. The grenades failed to explode or to disrupt the factory where President Radovan Karadzic prepared to give away his daughter Sonja, a failed rock-and-roll star, in marriage.

The offensive seemed to catch Western officials off-guard–despite conspicuous advances by the Bosnians over Debelo Brdo, or Fat Man’s Hill, a strategic high point near Sarajevo. “There’s just no consensus here on what they’re up to,” says a NATO planner. How about relief? Under siege for 38 months, Sarajevans have struggled for weeks without water, electricity, gas or food deliveries. A few small victories could add up to a big win on CNN–a court of international opinion throughout the Bosnian war. Other possible benefits: discomfiting the demoralized and overstretched Serbs and, perhaps, improving the Muslims’ odds at the bargaining table. A breakout might also free up the Bosnian army to assail other fronts.

Yet there’s something odd about this. Few military experts believe that the Muslims can sustain the fight. True, thanks to a U.S.-brokered alliance with the Bosnian Croats last year, the Sarajevo government is flush with small arms and some 80 tanks: Bosnian troops last Thursday liberated 40 heavy mortars from Ukrainian peacekeepers at the Marshal Tito Barracks in downtown Sarajevo. But the government forces remain considerably outgunned by the Serbs, who began taking back heavy weapons when they started kidnapping U.N. soldiers; they now have hundreds of tanks and up to 800 big guns ringing the capital. The Serbs haven’t been shy about using their stuff: in one day last week, artillery shells and sniping killed 11 people, including two patients in Kosevo hospital. Under these circumstances, say Pentagon analysts, the Muslims’ best bet may be to use mortar fire to force the Serb gunners to keep their heads down, while Bosnian infantry try to scale and take those positions-which requires flawless coordination, previously beyond the Bosnian forces. Alternately, the Muslims could try to pry open and hold a lifeline route into Sarajevo. Such a move would invite a costly Serb reprisal against civilians there. Still, “the Muslims may think that’s a price worth paying,” says one army source.

The prospects for a settlement look as grim as ever. “At the moment,” says Carl Bildt, the new European Union negotiator, “we’re heading toward war.” The Serbs, who promised on Saturday to release all remaining U.N. hostages, see the tide turning against them, and could be in a mood to deal. The Bosnians aren’t willing to talk peace–as long as they keep gaining and getting help from the Groats. “It’s going to be one helluva summer,” predicts a senior NATO official. If so, the West might not stick around long enough to feel the heat.