When United Nations Secretary-General Kofi Annan opined last week to the BBC that the American led overthrow of Saddam Hussein had been “illegal,” two words came instantly to my mind: baby food.

No, I’m not comparing Mr. Annan’s thoughts to pabulum. He is a smart man, adept enough that even in his BBC moment of condemning America, perhaps mindful that America is the U.N.’s chief financial backer, he took the trouble to blur responsibility for his own words, amending his use of “I” to the royal “we.” Said Mr. Annan: “From our point of view, from the charter point of view, it was illegal.”

It’s unclear exactly whose collective view Mr. Annan thinks he was authorized to express, or under what terms in the U.N. charter he casts himself on some occasions as the hapless servant of the Security Council, and at other times, such as this, as the outspoken chief judge of world law.

But if Mr. Annan wants to discuss right and wrong in Iraq, which seems to be the real issue, then it is time to talk about baby formula. Why? Because Mr. Annan’s preferred means of dealing with Saddam was a mix of U.N. sanctions and the U.N. relief program called oil-for-food. And the heart and soul of oil-for-food was supposed to be the feeding of sick and hungry Iraqi babies – including the purchase by Saddam, under U.N. auspices, of large amounts of baby formula. When oil-for-food was launched in 1996,it was advertised by the U.N. as a response to such horrors as pictures of starving Iraqi children and alarming statistics about infant mortality in Iraq, released by one of the U.N.’s own agencies, Unicef.

It was in service of that U.N. mix of sanctions and humanitarian relief that Mr. Annan, after visiting with Saddam in Iraq in 1998, returned to New York to report: “I think I can do business with him.”

And, oh, what a lot of business the U.N. did. Mr. Annan’s Secretariat collected more than $1.4 billion in commissions on Saddam’s oil sales, all to supervise the integrity of Saddam’s $65 billion in oil sales and $46 billion in relief purchases. The official aim of this behemoth U.N. aid operation was solely to help the people of Iraq, while the U.N. waited for sanctions to weaken Saddam enough so he would be either overthrown from within or forced to comply with U.N. resolutions on disarmament. Instead, Saddam threw out the U.N. weapons inspectors for four years, and, by estimates of the U.S. General Accounting Office, fortified his own regime with at least $10.1 billion grafted and smuggled out of oil-for-food.

But of all the abuses of oil-for-food committed by Saddam – and not only allowed but also in effect approved and covered up by Mr. Annan’s U.N. – the most cynical has to have been the trade in baby formula. This was one of Saddam’s imports that few even among the U.N.’s critics dared question. Who could be so heartless as to object to food for hungry children? And given the secrecy with which Mr. Annan ran oil-for-food – as hapless servant of a Security Council packed with big-time business partners of Sad dam, such as France and Russia – no one outside the U.N. except Saddam and his handpicked contractors knew much in any event about Baghdad’s traffic in baby formula.

The U.N. insisted that the identities of Saddam’s contractors and the terms of his deals remain confidential. Even today, though the names have leaked, many of the vital details of these contracts – such as quantity and quality of goods – remain smothered in the continuing secrecy imposed by the U.N.-authorized investigation into oil-for-food, led by former Fed chairman Paul Volcker. And Mr. Volcker, apparently focused mainly on bribery allegations involving officials of the U.N. itself, may never get around to such broader but also important matters as oil-for-baby-food.

But since Saddam’s fall, a few windows have opened through which one can glimpse Saddam’s U.N.-approved trade in nursery nutrition. Chief among them is a pricing study carried out by the U.S. Defense Department’s contract auditing agencies last year, shortly after Saddam’s overthrow. Lest anyone suspect the Pentagon of bias, it would of course be handy to draw on other studies as well. But there are none. Mr. Annan’s Secretariat, while swimming in cash from its 2.2% commission on Saddam’s oil sales, never got around to systematically examining Saddam’s contract prices. That was a notable omission, given that Saddam’s scam on relief contracts was one of the oldest and simplest in the book: overpaying for goods, using relief funds meant for the Iraqi public, then collecting part of those overpayments in the form of kickbacks.

And when it came to overpricing, which any veteran aid worker should surely recognize as a flashing red sign of probable graft, one of the most roundly abused categories under oil-for-food appears to have been the original rationale for the program: food itself.

The Pentagon pricing study looked at a sample of 759 big-ticket oil-for-food contracts still awaiting full delivery when Saddam fell – a snapshot of the program in its final years. Among those were 178 contracts for food. Of these, almost 90% were overpriced by an average of about 22% – more than twice the 10% figure often quoted as Saddam’s standard kickback. In this sample, totaling $2.1 billion in U.N.-approved grocery shipping by Saddam, the potential rake-off totaled $390 million.

And within that oil-for-food sample shopping spree, the baby formula deals were estimated to be even more egregiously overpriced than the average contract for most other staples. Compared to the hundreds of baby food and milk contracts in the overall program (many of those with France and Russia) the Pentagon sample was small. The study looked at four baby formula contracts, two originating in Egypt, one in Tunisia, and one in Vietnam – totaling $43 million, which in any normal relief program might actually rank not as a small sample, but as a lot of money. But it seems telling that every single one of those four baby-formula contracts appeared “potentially overpriced” by about 26%, for a total of $11 million in potential overpayments. On the biggest of these sample contracts, a $26 million deal between Saddam and a Vietnamese dairy company – approved by the U.N. in October 2002, in the thick of the U.N. debate over going to war to remove Saddam – the estimated overpricing of 26% worked out to well over $5 million on that contract alone.

Translation: In late 2002, while Mr. Annan was lobbying against American-led removal of Saddam, he was running a U.N. program in which money meant for baby formula, among other goods, was very likely flowing into the pockets of Saddam and his sons and cronies.

Somehow, that was the kind of problem that Mr. Annan’s office managed to miss, although according to a November 2002 statement to the Security Council by oil-for-food director Benon Sevan, U.N. staff in Iraq had by then made 1,187,487 total “observation visits” to ensure the integrity of oil-for-food. More than 1 million of those observation visits were devoted to checking on food and nutrition, and all of them were paid for out of the U.N. Secretariat’s 2.2% oil sales commissions from Saddam.

In the same November 2002 statement, Mr. Sevan reported that “acute malnutrition” was still rampant among young children in Iraq. Mr. Sevan explained that although malnutrition had been halved since oil-for-food began – all this was based on Saddam’s statistics – it was still double the rate of 1991 – a situation Mr. Sevan himself described as “far from satisfactory.” But the solution prescribed by Mr. Annan was not to spot and stop the kickbacks. Rather, while lamenting what he described in November 2002 as the “dire funding shortfall” of oil-for-food, Mr. Annan’s solution again and again was to urge more oil sales by Saddam. Which meant, most likely, more resources earmarked to feed babies but diverted to the Baghdad regime, and, by extension, more commissions for the U.N.

It would be interesting for someone with full access to the contract details – meaning, I suppose, the UN’s own investigation into itself – to total the scores of oil-for-food contracts for baby formula, weaning cereal, milk, and so on – much of it bought from Security Council member nations Russia and France – and employ some pricing experts to fill in the rest of the numbers.

But what we know already is that Mr. Annan, whose Secretariat turned a blind eye to Saddam’s food-pricing scams, has never apologized for presiding over the biggest fraud in the history of relief. He has not used the word “illegal.” The closest he’s come has been to admit this past March, after much stonewalling, that there may have been quite a lot of “wrongdoing”- before turning over the whole mess over to a U.N. investigation that has since smothered all details with its own blanket of secrecy.

Mr. Annan is due to step down next year. If he wants to leave a legacy more auspicious than having presided over oil-for-fraud, he might want to devote his twilight time at the U.N. to mending a system in which a U.N. secretary-general feels free to describe the overthrow of a murderous tyrant as “illegal,” but no one at the top seems particularly bothered to have presided over that tyrant’s theft of food from hungry children.

Ms. Rosett is a fellow at the Foundation for the Defense of Democracies and the Hudson Institute. From www.OpinionJournal.com. ©Dow Jones & Company Inc.