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Cutting back on salt is a key recommendation in the government’s latest Dietary Guidelines for Americans (DGA) and has been a part of good health advice for decades. But, increasingly, the evidence suggests that that guidance may be too simplistic, and that there is a limit to the benefits of salt reduction on the heart.

For people at risk of heart disease, a new study finds, lowering sodium can actually harm their health. Researchers led by Martin O’Donnell, an associate professor at McMaster University in Toronto and a professor of translational medicine at the National University of Ireland, looked at data on more than 28,000 people with heart disease or at high risk of developing heart disease or diabetes, and found that both those who consumed too much sodium and those who consumed too little had increased risks of heart disease and heart-related death over the study’s four-and-a-half year follow-up.

The government currently advises adults to eat no more than 2,300 mg of sodium a day, and recommends that children, older Americans and those at risk of heart disease cut their sodium to 1,500 mg a day. The World Health Organization advises eating less than 2,000 mg a day.

Participants in the study, whose salt consumption was measured by the levels of sodium in their urine (most of the salt we eat is excreted), consumed on average 4,800 mg a day. When researchers compared the heart risks in the highest consumers (7,000 mg to 8,000 mg a day) to those at a baseline 4,000 mg per day, they found that high salt consumption led to a 9.7% increased risk of dying from a heart event and a 7% increased risk of having a heart attack.

But people who excreted far lower amounts of sodium in their urine — between 2,000 mg and 3,000 mg a day — also raised their risk of dying from a heart event by 8.6% and their risk of being hospitalized for congestive heart failure by 5%.

MORE: Salt: How Bad Is It Really?

The lesson, says O’Donnell, is that the relationship between sodium and heart disease may not be the linear, as most of the public and public health officials have been led to believe. Instead of assuming that increasing sodium increases heart disease and heart-related deaths, the association may follow more of a J shape, in which very low levels of sodium also raise the risk of heart trouble — not as much as too-high levels of sodium do, but it results in a spike nonetheless.

“There is a lot of debate in the literature about this,” says O’Donnell. “Until now, the contention has been that the amount of sodium the body requires from the diet is very small. But our study and others published this year raise the issue that perhaps the amount the body requires for adequate physiological processing may actually be far higher than that.”

Recent research also hints that some people may be more sensitive to the effects of sodium than others, and that some may be able to take in higher levels of salt in their diet without experiencing negative health effects. Yet the public health message remains focused on lowering our sodium intake, since the bulk of the evidence still suggests that too much sodium leads to hypertension and may accelerate atherosclerosis and diabetes. But O’Donnell’s results now suggest that similar risks may hold at very low levels of salt intake.

MORE: Does Cutting Salt Really Improve Heart Health?

What does it mean for the average person who isn’t overconsuming salt — is lower still better? “We need to understand whether reduction of moderate-to-low levels of sodium intake translate to long-term effects in preventing heart-related events. We believe that is still an open question,” says O’Donnell. “We need to further understand how some populations are vulnerable to extremes of sodium.”

Of course, the average American is probably eating too much salt — maybe without realizing it, since salt is added to nearly every processed or prepared food that we buy. A good first step to controlling sodium intake, nutritionists say, is to take the salt shaker off the table. Then start paying attention to food labels, which indicate how much sodium is in the packaged foods you buy. Adding more fresh fruits and vegetables to your diet can also naturally help you reduce consumption of high-sodium foods and curb your cravings for salt.

The new study was published in the Journal of the American Medical Association.

Alice Park is a writer at TIME. Find her on Twitter at @aliceparkny. You can also continue the discussion on TIME’s Facebook page and on Twitter at @TIME.