Gabriela Pineda has her cap adjusted by fellow Edward C. Mazique Parent Child Center Head Start graduate Brhane Gezahagne. (Amanda Voisard/For The Washington Post)

Maybe, just maybe, we’re on to something when preschoolers are asking for seconds of broccoli. This, they swear, is the case at the Head Start program at the Edward C. Mazique Parent Child Center in Logan Circle, which I visited last week.

“Fresh broccoli — they eat it like candy,” head cook Evon Gaither told me in the center’s full-service kitchen. “They love collard greens. And last week, I stir-fried squash. They loved that.”

Now, even some grown-ups, most famously former president George H.W. Bush, have trouble choking down the much-maligned member of the cabbage family. So I’m not about to drink the (unsweetened) Kool-Aid and believe that little kids will beg for broccoli if only we’d offer it to them.

But something has to explain last week’s encouraging report out of the Centers for Disease Control and Prevention that, for the first time in decades, obesity declined among low-income preschoolers in 19 states and U.S. territories. One possible reason cited by CDC officials: the recent wider availability of fresh fruits and vegetables, instead of sugar-laden juices, for poor kids enrolled in a federal nutrition program.

So I went over to Mazique to see how they handle food and fitness, and I came away impressed by the rather simple principle they live by: Cultivate the habit of exercise and healthful eating while the children are young. Really young, like 6 weeks to 4 years old.

This is a heck of a good idea. One in eight U.S. preschoolers is obese; for black and Hispanic kids, the situation is worse. Children are five times as likely to be overweight or obese when they grow up if they have weight problems between ages 3 and 5.

Mazique kids don’t go home to nannies who cook them balanced meals and after-school sessions with personal trainers. “We serve the poorest of the poor,” Executive Director Almeta R. Keys said, adding, “And they don’t have the same advantages that other families do.” Some of the 4-year-olds I watched showing off their skills in English, Spanish and Amharic at last week’s graduation ceremony were homeless or living in transitional housing, she said.

So if anyone is going to make a difference in these kids’ lives, it’s their parents and the teachers at Mazique. Janet Unonu, who has been the program’s full-time nutritionist for 33 years, gave me a tour and the ground rules at the same time, starting with the small garden out front where the children help plant and harvest okra, basil and peppers that will later go into their meals.

Rice must be brown and bread the same color, she said. Baby food is made from scratch, ground from the same foods served to the older children. “From 6 weeks to 5 years [of age], they get no sugar here,” she said.

That’s not completely true. Once a month, the children get an oatmeal cookie containing sugar, Gaither said. (I consume more sugar than that at breakfast every day.) And once a month they’re allowed a sweetened cereal. The rest of the time, it’s fresh fruit for dessert and healthy grains at breakfast.

I wandered into a class of tots between 16 months and 2 years old, where the kids and teachers were eating family-style around those little preschool tables I couldn’t fit under if I tried. In the middle was a big bowl of fresh green beans; also on their plates were tuna fish and fruit. Milk at Mazique is low-fat.

What about exercise? The kids love Zumba, teacher Reby Franklin said, as well as other kinds of dancing or just jumping up and moving around. Parents are invited to participate. Teachers also take the kids on daily walks.

Is any of this going to stick when the little ones move on to a world of fast-food ads and video games? Mazique is hedging its bets. Parents are encouraged to take a six-week course offered by the program that teaches them how to read food labels at the store and cook healthful meals at home. They also are taught how to get kids exercising at home.

Meseret Abebe, whose 4-year-old served as mistress of ceremonies at the graduation, said she has learned to look for no-sugar-added juice and 2 percent milk. There’s no soda, chips or sweets in her house, and no fast food. She tries to serve fresh vegetables three times a day.

One day, Secretary of Agriculture Tom Vilsack visited Mazique and was pleased to see some of the children ask for seconds of broccoli, Keys recalled. Maybe this is a partisan thing. As President Obama noted just last month, it’s his favorite food. Not just his favorite vegetable, his favorite food.

I’m going to have to stick with chocolate chip cookies on this one. But don’t tell the kids.

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Remember my friends Gerry and Bridie Dunn, the father and daughter who started diving together at the Kennedy Shriver Aquatic Center in North Bethesda last fall? They’re just back from South Korea, where Gerry took two silver medals in Masters competition, and Bridie won three golds diving in an under-40 division. Congrats!