LONDON — The leading question about President Bush’s “surge” of 21,500 reinforcements in Iraq, comprising five Army brigades and two Marine battalions, is how these formations will be employed.

It is believed that General Petraeus, who has been put in charge of the reinforcement, will use them to increase American strength in Baghdad itself and in Anbar province, the area to the west of the city where the Sunni insurgents are particularly active.

It is also believed that General Petraeus will implement new tactics. He has been impressed by a study of counterinsurgency methods circulating in the Pentagon, based on methods used by the British in Malaya and the French in Algeria, both in the 1950s and 1960s. Unlike the methods used so far in Iraq, which have relied on heavy force to meet and defeat insurgent bodies, the Anglo-French approach was to send in a separate group of units that familiarized itself with the geography of the troubled spot, got to know the inhabitants, and tried to understand their habits and culture, so as to use local tradition for counterinsurgency purposes.

The method, known as “hearts and minds” to the British and “special administration” to the French, proved remarkably successful, particularly when combined with the movement of dissident groups of the population to new living areas.

The method is financially costly and time-consuming, but the president has made available $1 billion to the surge.

The method also requires soldiers to adopt a cooperative and understanding approach to the people among whom they operate, but experience suggests that, once learned, the approach comes naturally to soldiers and is less wearing than the practice of constant aggression and the heavily reactive response to insurgent incidents.

General Petraeus has experience of using the method in eastern Iraq earlier in the American deployment and achieved great success. The area that he pacified remains calm to this day.

“Hearts and minds” is unfamiliar and even alien to the American armed forces, which traditionally operate on the principle of maximum force, with a heavy emphasis on self protection.

At the outset, it may result in a rise of American casualties, since it requires troops to move among the population and to expose themselves to attack. But it also yields plentiful intelligence, the key to success in counterinsurgency. It will also prove valuable to the “surge” reinforcement that they will not be involved in any of the routine activities — such as convoy protection, which absorb large numbers of coalition troops on a daily basis — but will be at liberty to concentrate on specific counterinsurgency tactics.

The White House and the Pentagon will be watching the progress of the reinforcement operations keenly, since this may be the last increment of force that the president is able to deploy.

Given the current state of overstretch in the American Army and Marine Corps, the availability of uncommitted reserves is shrinking.

So, too, is the tolerance of Mr. Bush’s political opponents as well as that of the American people. A great deal is riding on the surge. If it succeeds, many in the press will ask why the new tactics were not tried before. If it fails, the administration’s whole military and foreign policy will be put at risk.