There are three basic arguments to be made in favor of organic food: it’s better for the land, it’s lower in pesticides, and it’s better for you. In the war to win the hearts, minds, and dollars of consumers, a lot of producers, marketers, and retailers have been counting on that third case—that organic food is more nutritious.

It’s not easy to prove though, which is why there was considerable excitement this week when the British Journal of Nutrition published a pair of meta-studies (each aggregating the results of hundreds of original studies) concluding that organic meat and milk do indeed have nutritional advantages over conventionally produced products. The study finds that organic dairy and meat contain about 50 percent more omega-3 fatty acids (a desirable substance), while organic meat also contains slightly less of two saturated fats that have been linked to cardiac disease.

“Omega-3s are linked to reductions in cardiovascular disease, improved neurological development and function, and better immune function,” study co-author Chris Seal, a professor of food and human nutrition at Newcastle University in the UK, told NPR’s The Salt. So we think it’s important for nutrition.”

Nobody wants to argue with healthier meat and milk, but as the week progressed, a few less-enthusiastic voices emerged to raise important points:

1. You don’t benefit from what you don’t consume.

Ian Givens, professor of food chain nutrition at the University of Reading, interviewed for a terrific article in the Telegraph, said the increase in omega-3 was observed in milk fat, not the milk itself, so switching would represent only a small change in health benefits, especially given how much of the population still drinks low fat milk.

2. “Fifty percent more” is not the same as “a lot.”

Milk and beef aren’t particularly good sources of omega-3s in the first place. Richard Bazinet, a professor of nutritional sciences at the University of Toronto, told the New York Times News Service that you need to add 200 milligrams a day of omega-3s to an average diet to yield health benefits. Switching to organic beef would add about 50 milligrams. “Eating one grass-fed beef serving per day is not going to do it,” he said. There are far more effective alternatives, including seafood, nuts, and seeds.

3. It’s not the organic, it’s the grass.

Ian Givens explained to the Telegraph: “Differences in content such as fatty acids or iodine occur primarily because organic animals are fed more of a forage-based diet, such as grass, than their non-organic counterparts.

“You get the same kind of changes in food composition if non-organic animals are fed forage-rich diets too. It’s the choice of feed, not the organic farming method, which makes the difference.”

4. There’s more to food than omega-3s.

As the researchers themselves point out, the studies they reviewed for their analyses don’t have much to say about human outcomes, and there’s a lot going on in food. For example, conventionally grown milk is richer in iodine and selenium than organic milk. Is that more important or less than the omega-3s in organic milk? Does any of it make much difference at all in a reasonably well-balanced diet?

Stay tuned.