Some military officials involved in supplying the Iraqis describe the sense of urgency they felt and the need to cut through what they saw as a cumbersome military bureaucracy.

A few miles from Mr. Saffar’s armory, Maj. John Isgrigg III and Maj. Timmy W. Cox were assigned to issue weapons to the Iraqi military and national guard from early 2004 to 2005. As soon as they heard that a new shipment was arriving, the officers said, they put together a convoy to be the first to claim it, barreling onto the tarmac at Baghdad International Airport and loading the crates of Glocks and AK-47s.

In several telephone interviews and e-mail exchanges, Majors Cox and Isgrigg described a race between themselves and the system. They acknowledged that they did not do everything by the book. They did not always call ahead to the airport to say they were coming. They signed receipts but did not always wait around to fill out inspection reports, known as DD-250s. And they told only certain superior officers about their plans for where the weapons would be delivered.

Major Isgrigg, 46, described the chain of custody as a maze of red tape. Once weapons went into it, it took days for them to be released, he said. Sometimes, he said, a competing unit distributing weapons to the Iraqi police would get to a shipment first, so he and Major Cox would have to wait for the next one. He said that warehouse crews had been infiltrated by Iraqis sympathetic to insurgents, and that sometimes weapons would disappear.

“We had folks getting killed because equipment wasn’t moving,” said Col. Randy Hinton, the majors’ superior officer. “Were there times when all the right forms were not signed? Probably. But we had a mission to do, and we were going to do it the best way we could at that time.”

In a phone interview from Bangkok, John Hess, who worked as the assistant director of operations for an American-owned company that helped manage supplies for Iraq, said payments to the companies that supplied arms to Iraq were often delayed because of missing DD-250s. He said he believed that the officers had the right motives but used dangerous methods.

“Once those weapons left normal channels,” Mr. Hess said, “none of us were ever sure where they were really going.”