The correlation that Holmes and her collaborators hit upon persisted even after they controlled for people’s age, gender, race, parental status, and other demographic variables (though they did not calculate how the optimal amount of free time varied depending on these factors). The researchers write that their finding is a “small” effect, but still significant, considering that “there are a slew of other variables that play into people’s overall assessment of their satisfaction in life.”

An experiment that the researchers arranged hinted at a possible explanation of the correlation they found. They asked participants to picture and describe what it would be like to have a certain amount of daily free time, and then report how they’d feel about that allotment. “What we find is that having too little time makes people feel stressed, and maybe that’s obvious,” says Holmes. “But interestingly, that effect goes away—the role of stress goes away—once you approach the optimal point.” After that point, Holmes says, the subjects started to say they felt less productive overall, which could explain why having a lot of free time can feel like having too much free time.

It’s not clear what an individual is to do with these findings, since the amount of free time people have usually has to do with a variety of factors, such as having children or a degree of control over work schedules. That said, Holmes told me that she shared her research with the MBA students in her class on happiness, and some of the most time-crunched among them were comforted by the findings: “I think that two and a half hours creates a nice goal that, even if you increase a little bit more of your discretionary time use, you [can expect] that it will translate into greater life satisfaction.”

Daniel Hamermesh, an economist at the University of Texas at Austin who studies time use, said it can be difficult to suss out the relationship between free time and life satisfaction. For one thing, some of the data analyzed in the paper was obtained by asking people to estimate how much free time they have, and those estimates can be unreliable. For another, it’s difficult to systematically say what qualifies as “discretionary” time and what doesn’t. “Every minute we have is subject to choice one way or the other, consciously or not,” he notes.

While Hamermesh didn’t inspect the underlying data in the paper, he offered a couple of possible (but, he notes, hard-to-test) explanations for the findings. “Let’s say everybody around me has two hours of discretionary time, and for some reason I have four,” he says. “I have no friends to play with”—his point being that people’s free time might be less fulfilling if they can’t spend it with others.

Another theory: Having too much free time might challenge a person’s self-image. For a man who provides for his family, Hamermesh says, “if I have so much time that I can spend it on, I don’t know, watching television, maybe I feel I’m not a real man.” (This feeling could be related to the pressure many people feel to appear useful and in demand as they vie for work in a competitive labor market.)