The latest comparison between Vietnam and Iraq goes like this: David Petraeus is another William Westmoreland, another general who spoke optimistically about a doomed war in order to serve the president’s political purposes. Similar lines have also been drawn from General Petraeus to General Westmoreland’s predecessor, General Paul Harkins, and to General Westmoreland’s successor, General Creighton Abrams. This reasoning rests upon notions about the Vietnam War that have withered under study by historians. And it betrays a misunderstanding of a military commander’s duties.

David Halberstam and Neil Sheehan produced the portrait of a hopelessly optimistic General Harkins. After General Harkins declared that the South Vietnamese had won the Battle of Ap Bac in 1963, Messrs. Halberstam and Sheehan decided that General Harkins was reflexively dismissing anything that ran contrary to official optimism. Messrs. Halberstam and Sheehan had decided that Ap Bac was a disastrous South Vietnamese defeat from listening to Lieutenant Colonel John Paul Vann, who grossly exaggerated South Vietnamese mistakes to conceal that he had committed the biggest tactical mistake of the battle. As Colonel Vann himself acknowledged, estimated enemy fatalities at Ap Bac exceeded South Vietnamese fatalities.

It is true that General Harkins was disappointed with the performance of two South Vietnamese commanders at Ap Bac, but he did not say so publicly. What he appreciated and what the press failed to appreciate was that public criticism would cause America’s allies to lose face, no small matter in an East Asian country, and would undermine military and civilian morale. Unbeknownst to the press, General Harkins worked behind the scenes to get the two commanders relieved.

For reasons of morale, wartime military leaders the world over emphasize the positive even on the darkest days. General Eisenhower explained that as Supreme Commander of the Allied Forces during World War II he always maintained an upbeat outlook because “without confidence, enthusiasm, and optimism in the command, victory is scarcely obtainable. … Optimism and pessimism are infectious and they spread more rapidly from the head downward than in any other direction.” Contrary to what one often hears today, the war in South Vietnam as a whole was not always going poorly. Recent disclosures from Communist sources have validated General Harkins’s belief that the South Vietnamese held the upper hand from early 1962 through October 1963. The war did not turn sour until the overthrow of the president of South Vietnam, Ngo Dinh Diem, on November 1, 1963. The coup replaced a strong man with weak ones and produced purges. Several years of military decline followed.

Criticism of General Westmoreland’s public optimism has centered on his November 1967 assertion that light lay at the end of the tunnel and American troops could begin turning the war over to the Vietnamese within two years. When the Tet Offensive erupted in January 1968, many in the press and Congress decided that General Westmoreland had been utterly wrong. In actuality, Communist forces had been reeling before Tet, and they suffered a crippling blow during Tet. That defeat and the subsequent rejuvenation of the South Vietnamese allowed the United States to begin withdrawing troops even sooner than General Westmoreland had predicted.

When General Creighton Abrams talked of dramatic improvements in the South Vietnamese armed forces from 1969 to 1971, charges of “mindless optimism” flew across Washington and New York. But the South Vietnamese justified General Abrams’s remarks. They wiped out the remnants of the Viet Cong insurgency during those years. Demonstrating impressive courage and skill, they foiled a North Vietnamese Army invasion in 1972. They might well have done the same to North Vietnam’s even larger 1975 offensive had the U.S. Congress not slashed support.

A military sage once said that if you think you are going to lose, you are going to lose. In the daunting business of war, a country does far better with a military commander who thinks he can win and finds ways to get tasks done than with a commander from the Harry Reid School of Leadership who only finds reasons why tasks can’t be done. A commanding general must be able to recognize that some tasks are impossible. If our commanding general in Iraq believes success is unattainable and we should get out, then he ought tell it to the president or others in his chain of command behind closed doors. He must not announce it to the whole world. If the president chooses to keep fighting after receiving such a warning, the military commander must either get behind the president’s policy or step aside. That is what civilian control of the military necessitates.

Mr. Moyar is the author of “Triumph Forsaken: The Vietnam War, 1954-1965.”