Statues of Saddam Hussein were destroyed in Baghdad, and Iraqis kissed American Marines and soldiers in the streets. Yes, the celebrations hide the darker reality of chaos and looting. And yes, fighting still goes on all over Iraq (as indeed it does in Afghanistan).

But if these things are real, so is the larger victory. A tyrant has been ousted in Iraq, and the people danced in the streets for joy that he was gone. Whatever your position on the decision to go to war, this is a cause for great rejoicing.

It is precisely such moments that show the nobility of the military's purpose — which is, as the Pope once put it, to be “an encouragement to everyone not to be resigned to injustice but to conquer evil with good.”

Another reason to cheer: The conduct of this war has been as careful as any military offensive in memory. Our troops went to great lengths to keep civilian casualties at an absolute minimum. We can be proud of America, a nation that values the lives of innocents in war.

So, in the wake of this new victory, what do we say of Pope John Paul II? What now of his now-famous assertion that “no problem is solved by war”? Has he been proved wrong?

We mustn't forget — he certainly doesn't — that the Pope was a seminarian in Poland on its own National Liberation Day, July 22, 1944. As George Weigel wrote in Witness to Hope, “The young seminarians, having survived the Occupation, might have imagined that a return to normality in a free and independent Poland was at hand. If they did, they were quickly disabused of the notion.”

No other nation suffered as much at the hands of the Nazis as Poland did. But the defeat of the Nazis only brought Soviet-inflicted suffering. Decades later, the celebration of National Liberation Day was quietly taken off many Polish calendars when real freedom was won there, peacefully, by the Pope and his allies.

Certainly, the United States can't be compared to the occupying army of Soviets in Poland. Our plan is to liberate the people, help them on their first fledgling hops to freedom, then depart. But that's exactly why the next step for Iraq is so dangerous.

For decades, Hussein's government favored Sunni Muslims, who account for only 20% of the nation's inhabitants, while suppressing Shi'ite Muslims, Kurds and Christians. What comes now is anyone's guess — and the 4% of the population who are Christians are particularly wary.

We hope that democracy comes next, but democracy is an elusive thing, particularly in a nation sharply divided along ethnic and religious lines.

And, sadly, despite unprecedented military efforts to avoid civilian casualties, there are horrors that have scarred Iraqi families deeply.

Thank God there weren't the sheer numbers of civilian casualties we saw in 20th-century warfare, but there were still many. Pictures of an Iraqi boy have become symbolic of them. His body burnt and his arms blown off, he cried out, “Can you help me get my arms back? Do you think the doctors can get me another pair of hands?”

Also, consider the blurring of lines between civilian and soldier that occurred in Iraq. Men and, just as often, boys were forced to fight for Saddam and were told that their families would suffer if they didn't. Many of them are now dead.

And one last sign of the struggle ahead: There are already moves afoot in Planned Parenthood, aid agencies and the U.S. Senate to start “Operation Iraqi Freedom to Choose” and bring abortion to Baghdad.

Don't get us wrong. April 9 is a truly historic day for Iraq. Saddam, it seems, is gone. War eliminated a major source of Iraq's woes, and that's a very good thing indeed.

But war didn't solve Iraq's problems. Let us pray for the kind of peace that will.