To Fight Obesity, a Carrot, and a Stick Childhood obesity, at long last, may have peaked - even among the poor, where the problem is most prevalent. Between 2008 and 2011, according to a study from the Centers for Disease Control and Prevention, 19 states and territories saw a small but significant drop in obesity rates among low-income preschoolers. This is a problem that many people assumed would only get worse. So how has this small bit of success been achieved? One factor is certainly an extensive behavior-change campaign; official America is now bribing, cheering and badgering us to eat fruits and vegetables, exercise, drink water instead of soda and cut down on screen time. Another is that cities and civic groups are doing creative things to bring healthier food to poor neighborhoods. These changes help. But there may be a more direct reason for the progress against child obesity. The C.D.C. study focused on preschool-age children, from 2 to 4 years old, most of them enrolled in the federal Special Supplemental Nutrition Program for Women, Infants and Children, known as WIC. WIC provides vouchers to pregnant and nursing women, and mothers of children under 5 to buy specific foods. In 2009, WIC changed its rules. There are new vouchers specifically for produce, for example. Milk must be reduced-fat, and bread and rice must be whole-grain. And stores participating in WIC must carry these items. You can see that change in corner stores and bodegas across the country, including, for example, Luciano Espinal's Deli Grocery, on Lehigh Avenue in North Philadelphia. Mr. Espinal's store has two aisles and a deli counter in the back. There are similar stores all over the neighborhood, their shelves filled with snack cakes, chips, soda, white bread. The only fresh foods are the iceberg lettuce and tomatoes needed by the deli counter, and maybe potatoes and onions. But Mr. Espinal's store accepts WIC vouchers. So he carries things non-WIC stores do not: apples, oranges, green peppers and bananas. He also carries the WIC-required whole-grain bread, brown rice and 2 percent milk. Of course, people could buy more of the unhealthy stuff with their own money. But the evidence says they don't. Yale's Rudd Center for Food Policy and Obesity looked at purchases by WIC participants in Massachusetts and Connecticut, including what they bought with their own cash. After the WIC changes, participants bought significantly more whole-grain bread and brown rice and reduced-fat milk, and far less white bread, whole milk, cheese and juice. Attitudes are changing. Access to healthy food is increasing. But that doesn't address what is probably the most important problem: cost. On a limited budget, people buy cheap and unhealthy food. Community groups and cities can't solve that problem - not for more than a handful of people at a time, anyway. But the federal government can. The success of the WIC reforms proves it. The program matters: half of all infants and a quarter of all children under 5 in the United States will be on it at some point. But with nine million participants, it is dwarfed by the Supplemental Nutrition Assistance Program, or SNAP - commonly known as food stamps - which reaches more than 47 million people. Food stamps keep people from starving. But you cannot buy fresh produce on $1.40 per meal. Let's contemplate the extra medical bills we'll be paying because of Congress's decision to let the Recovery Act's increases in food-stamps benefits expire. SNAP needs some help. One strategy is to provide financial incentives to buy fruits and vegetables. This is happening in many farmers" markets; Philly Food Bucks, for example, gives people a $2 coupon for every $5 in food stamps they spend on produce at participating markets. Food stamps sales at these markets have increased by nearly 400 percent. In some states, eligible produce must be locally grown, a change farmers appreciate. The idea is spreading to supermarkets. This summer the Agriculture Department released results of its Healthy Incentives Pilot in Hampden County, Mass. Supermarket shoppers earned 30 cents for each food stamp dollar they spent on fruit and vegetables. Those in the program bought 25 percent more produce than the control group, at a cost of 15 cents per day. These programs are lovely, but they reach relatively few people, and they are expensive. Another strategy is harsher: Copy WIC and limit the foods that food stamps can buy. Such a change could cover the whole country in one administrative stroke. And, of course, it is virtually free. With even more cuts in food stamps looming in the farm bill, that's important. Minnesota, Mississippi and New York asked the Department of Agriculture for permission to take soda or candy out of SNAP. Mississippi later withdrew its request. The department said no to New York, saying the program was poorly designed. It told Minnesota that the state could not change the federal program's definition of what could be covered. None of the obstacles to limiting food stamps to healthier foods seem insurmountable. It is administratively simple to draw a line. But not politically simple. It's not just that people on food stamps are an enormous market for soda and junk food. Big Soda has unusual allies. Restricting purchases is not controversial with WIC, which exists to supplement nutrition. But it is with food stamps, which exist to supplement income. "There are people in the anti-hunger community who support a soda tax in general because it affects everyone, but they oppose banning soda from SNAP because it affects only poor people," said Marlene B. Schwartz, director of the Yale Rudd Center. Their philosophical argument is, if it's the right thing to do for everyone, then make it for everyone. Other approaches exist. A portion of food stamps benefits could be set aside for produce. Or states could use the guidelines they already follow - to little controversy - with sales taxes. More than half the states tax soda or junk food at a higher rate than the food tax rate - in effect, they do not consider them food. "Instead of arguing about healthy versus unhealthy, I would almost rather say what counts as food," said Ms. Schwartz. States already figured out what is and isn't food.