KANDAHAR, Afghanistan  In the newly won districts around this southern city, American forces are encountering empty homes and farm buildings left so heavily booby-trapped by Taliban insurgents that the Americans have been systematically destroying hundreds of them, according to local Afghan authorities.

The campaign, a major departure from NATO practice in past military operations, is intended to reduce civilian and military casualties by removing the threat of booby traps and denying Taliban insurgents hiding places and fighting positions, American military officials said.

While it has widespread support among Afghan officials and even some residents, and has been accompanied by an equally determined effort to hand out cash compensation to homeowners, other local people have complained that the demolitions have gone far beyond what is necessary.

It would also seem to run counter to Gen. David H. Petraeus’s counterinsurgency strategy, which calls for respecting property as well as lives, and to run up against recent calls by President Hamid Karzai for foreign forces to lower their profile and avoid tactics that alienate Afghan civilians. There have been no reports of civilians casualties from the demolitions.