But, researchers say, not only would such a study be expensive -- the exercise groups would need constant support, and researchers would have to monitor how much they were exercising -- but volunteers would be unlikely to comply with their assigned regimens. Telling someone to exercise or to remain sedentary for years is not like telling her to take a pill.

The alternative is to look at populations of people who did or did not exercise and try to correct for factors that might be linked to exercise and to cancer. Exercisers might be thinner, for example, and if they had a lower incidence of breast cancer it might be body weight, not exercise, that was responsible.

Study after study was conducted: some found small protective effects of exercise on breast cancer; others found none.

Now, in Dr. Henderson's opinion, there is no point in continuing to ask the same question in the same ways.

"We've pretty much settled the issue that there is a small effect," he said. The effect, Dr. Henderson added, is so small, that even if it is real, it makes little difference to an individual woman. In one of his studies, the effect of exercise was so small that if he took into account alcohol consumption -- which has been associated with a slightly increased breast cancer risk -- the exercise effect went away.

"If you are going to exercise, there are other good reasons," Dr. Henderson says. "But protection from breast cancer is not one of them."

Dr. McTiernan has a different view. Instead of continuing to ask if there is a correlation between exercise and breast cancer, she said, she has been asking, "What are the biochemical changes that occur with exercise and could they affect a woman's risk?"