TIME: On Scene -- Highs and Lows in Baghdad  

What does it actually mean to win the war in Iraq?

The war grinds on. In Baghdad, a capital desperately seeking a sense of normalcy in the midst of a long and brutal insurgent war, it's taken close to 40,000 American soldiers and Iraqi security forces to keep al-Qaeda's suicide bombers at bay. For the past five days the Baghdad garrison, reinforced with the added muscle of eight battalions pulled in from across the country, plus one more flown up from a forward force base in Kuwait, had patrolled a city free of car bombs or men with explosives strapped to their chests. But on Thursday, the carnage returned, when three bombers found their targets: a funeral procession, a security checkpoint, and the headquarters of the police major crimes unit. At least 56 people died. While the insurgent enemy's ability to operate had been badly crimped since March 12 by the sprawling urban offensive dubbed Operation Scales of Justice, a candid Major General Rick Lynch -- the official U.S. military spokesman in Iraq -- admitted, "Today he found gaps."

Still, despite the horror of flames, torn flesh and twisted wreckage staining busy streets, the day was not without marvel. Thursday morning witnessed the realization of one of those rare, wistful hopes every Westerner in the country holds deep within them -- that hostages, trussed and secreted away in some anonymous hide, could be surprised by soldiers from home bursting in through the door and telling them it's going to be okay. In a house somewhere in the city's west, three devout aid workers from a faith-based outfit known as the Christian Peacemakers Teams -- Canadians Harmeet Sooden, 32, and Jim Loney, 41, and Briton Norman Kember, 74 -- were freed by British special forces and Canadian law enforcement. The raid, born of intelligence extracted from a freshly captured prisoner only three hours earlier, oddly found the kidnappers absent; alas it couldn't save Virginian Tom Fox, 54, whose tortured body had been found on a rubbish heap earlier this month.

Among the 430-odd foreigners kidnapped in Iraq so far in this conflict, only a few have been similarly rescued. By and large, the hostages are freed, for whatever reason, at the whim of their captors, or else murdered once their presence becomes too problematic or unprofitable. The taking of these harmless humanitarians served, if nothing else, to remind that there's only so far good intentions will take you in Iraq. That they bore no ill will, were staunchly non-violent, sympathetic to the Iraqis' plight, earnestly assimilating, and even anti-American in a barely veiled way, meant nothing. They were still snatched, still held for months, and Fox was still brutalized and executed. With ever more chilling surety, there is barely any quarter being given in this war. Every foreigner breathed a gentle sigh upon news of their rescue, paused darkly over the fate of Tom Fox, and held one more quiet thought for American journalist Jill Carroll, 28, still out there. Somewhere. Here, even high points come with jagged edges.

At the military's weekly press briefing, Gen. Lynch reminded reporters of the progress being made. The artfully persuasive general repeatedly insisted that 75% of the Iraqi troops and police required to hold the country together were now in place. Where there were 100,000 security personnel a year ago, now 241,000 are in the field, he said. A third of last week's operations had no Coalition thumbprint; they were conceived, planned and executed by Iraqis. Just over a third more were conducted jointly, leaving U.S. grunts to pound out less than a third on their own, a marked difference from a year ago. Two larger operations, one near the capital, the other to its north, had snared more than a hundred prisoners and some enemy weapons caches, he said. But sectarian killings were escalating, as extremists' death squads on both sides of a violent divide in one week are suspected to have left almost 134 bodies in the capital alone. "We are dealing with a vicious enemy," the general intoned, "now focused on inflaming sectarian violence."

Yet, with the war's fury concentrated primarily in three busy provinces, "the idea that all of Iraq is experiencing widespread violence is incorrect," he added. But after spending close to $250 billion, losing the lives of more than 2,300 U.S. troops, and three years of bloody effort, there's still no sign of winning. Indeed, Iraq may yet show a war can be won without actually winning it. GIs will go home once the Iraqis prove they can take over the fight. And that's not necessarily with the enemy being defeated. As long as the war can be handed over, whether the enemy remains or not, some will want to call it victory. With all the advances, great and small, the two-star general bluntly acknowledged one more telling statistic. Though attacks in the capital were down 10% in the past week, and car bombings dipped by half, there were still more than 500 attacks on Coalition troops nationwide. Americans or Brits are still being hit, on average, about 74 times a day, though only one quarter of those assaults are deemed effective. That's no real difference from a year ago, or even longer. The enemy, despite it all, seems little dented. Each success is hard fought in Iraq. And may not necessarily last long at all. As Lynch rightly puts it, "This is a tough business".