If you’ve ever doubted that a few healthy lifestyle changes can actually lower your risk of cancer, well, think again.

The authors of a new study suggest that 20 to 40 percent of cancer cases—and about 50 percent of all deaths from cancer—might be prevented if we all did these four things: exercise regularly, maintain a healthy BMI, stay smoke-free, and skip booze or drink only in moderation.

That’s it—or, rather, that might be enough to slash cancer rates and deaths, according to the research published today by JAMA Oncology.

While similar research on the link between cancer and lifestyle factors has been done in the past, “it’s been a while, and the lifestyle profile in the U.S. has changed dramatically,” said lead author Dr. Mingyang Song, of the Massachusetts General Hospital, Harvard Medical School, and Harvard T.H. Chan School of Public Health in Boston. “We want to provide an updated picture.”

But there was another reason behind Song’s research: It was done in response to a January 2015 study published in Science, which suggested that a third of the cancer risk across tissues in the body might be caused by the environment or genetics; and the rest might be caused by random DNA mutations in stem cells (in other words, bad luck). That finding, however, was misinterpreted by the media, and left some of the public thinking that most cancers themselves were due to random chance.

Song hoped to address that confusion with his current research, which examined more than 130,000 white people from two long-running studies: the Nurses’ Health Study (NHS) and the Health Professionals Follow-Up Study (HPFS).

The researchers divided the people into two groups, based on their lifestyle: The first was considered “low risk” (or healthier) and the second group, “high risk.” Then the researchers looked at how likely the people in each group were to develop cancers of the lung, breast, pancreas, bladder, and more. They didn’t include skin and brain cancer (among other types) since those cancers are strongly linked to causes like UV rays and other carcinogens.

It bears repeating that the study only included white people. Since the participants of the NHS and HPFS are predominantly white, the researchers chose to exclude “the small proportion of non-whites” to “avoid any influence that different ethnic distribution would make on our findings,” Dr. Song explains.

What they found: the low-risk group was less likely to develop and die from cancers than both the high-risk group and the general white population in the U.S.

And here’s the key: The people in the low-risk group shared the following four characteristics.

1) They didn’t smoke. More specifically, they either never smoked at all, or were smoke-free for more than five years.

2) They didn’t drink, or drank in moderation. Meaning the women had no more than one drink per day; and men had no more than two.

3) They had a healthy BMI. In this case, that meant a BMI between 18.5 and 27.5. (The Centers for Disease Control and Prevention classify a BMI over 25 as overweight.)

4) They exercised regularly. The study participants either exercised vigorously for 75 minutes a week, or did 150 minutes of moderate-intensity exercise.

Of course, this isn’t to say it’s easy to fit in 150 minutes of physical activity a week, or that maintaining a BMI in the mid-20s is a piece of cake. But it is heartening to know that the healthy goals we strive for are backed up by solid research—and well worth the effort.