But Kyle Flack, an assistant professor of nutrition at the University of Kentucky, began to wonder a few years ago if this outcome was inevitable. Maybe, he speculated, there was a ceiling to people’s caloric compensations after exercise, meaning that if they upped their exercise hours, they would compensate for fewer of the lost calories and lose weight.

For a study published in 2018, he and his colleagues explored that idea, asking overweight, sedentary men and women to start exercising enough that they burned either 1,500 or 3,000 calories a week during their workouts. After three months, the researchers checked everyone’s weight loss, if any, and used metabolic calculations to determine how many calories the volunteers had consumed in compensation for their exertions.

The total, it turned out, was an average of about 1,000 calories a week of compensatory eating, no matter how much people had worked out. By that math, the men and women who had burned 1,500 calories a week with exercise had clawed back all but about 500 calories a week of their expenditures, while those burning through 3,000 calories with exercise ended up with a net weekly deficit of about 2,000 calories. (No one’s overall metabolic rate changed much.)

Unsurprisingly, the group exercising the most lost weight; the others did not.

But that study left many questions unanswered, Dr. Flack felt. The participants had performed similar, supervised workouts, walking moderately for 30 or 60 minutes, five times a week. Would varying lengths or frequencies of workouts matter to people’s caloric compensation? And what was driving people’s eating? Did the differing amounts of exercise affect people’s appetite hormones differently?

To find out, he and his colleagues decided to repeat much of the earlier experiment, but with novel exercise schedules this time. So, for the new study, which was published in November in Medicine & Science in Sports & Exercise, they gathered another group of 44 sedentary, overweight men and women, checked their body compositions, and asked half of them to start exercising twice a week, for at least 90 minutes, until they had burned about 750 calories a session, or 1,500 for the week. They could work out however they wished — many chose to walk, but some chose other activities — and they wore a heart rate monitor to track their efforts.