(CNN) After years of bad news about the obesity epidemic, which affects one-third of Americans, things may finally be looking up. In the past 10 years the rates of obesity appear to be leveling off among both children and adults .

The reason for the possible turn in the obesity tide appears to come down to what experts always suspected it would: eating fewer calories. One recent study found that the average adult went from consuming 2,220 calories a day in 2003 to 2,134 in 2010

There are already hints of some of the other health payoffs of reducing calories. "In addition to improvements in obesity, there is evidence that we have avoided vast numbers of premature deaths," probably by reducing heart disease, diabetes and other conditions, said Dr. Walter Willett, professor of nutrition and epidemiology at Harvard T.H. Chan School of Public Health.

Even more encouraging is that Americans appear to be cutting calories in the places they should. They are having fewer sugary drinks , and all but nixed trans fats, even before the recent federal ban.

Yet, Americans still have a long way to go in how they divvy up calories to get their plates to look more like My Plate , the Department of Agriculture's guideline for healthy eating.

"There has not been a big enough change in sugar-sweetened beverages and refined carbohydrates and fast foods, and there has not been an increase in the healthy foods," said Barry Popkin, distinguished professor of global nutrition at the University of North Carolina. "We have slightly cut our calories [but] we still consume over half our calories from the wrong foods," he said.

Experts hope, however, that the small improvements in recent years are just the beginning of a calorie-swapping trend. "I think we are seeing a cultural change like we have with smoking," Willett said. "I think we reached a tipping point that will accelerate the decrease in sugary drinks," and also lead to an increase in the consumption of healthy foods, he added.

Sodas and fruit juices way down, water way up

Americans in almost every age and ethnic group have been weaning themselves off soda and fruit drinks. A study of nationwide diet surveys found that children and adults consumed an average of about 155 and 151 calories, respectively, from these drinks in 2010, down from 223 and 196 calories in 1999. Both at home and when eating out, during meals and at snack time, they reported passing on these beverages.

In most cases, Americans are substituting soda for healthier choices . "As [sugar-sweetened] beverages have been going down, water is zooming right up, and that is split between tap water and bottled water," about 60-40, said Adam Drewnowski, director of the Center for Public Health Nutrition at the University of Washington School of Public Health. "That's a good thing," he added.

Although consumption of energy drinks and sweetened teas and coffees rose between 1999 and 2010, these drinks made up a small percentage of calories that Americans get from sugary drinks.

All this is good news, but it is not enough. "We are getting a little closer on sugary beverages, but not anywhere close to where we need to get," Popkin said. Most (60%) of Americans still consume 230 calories or more a day of added sugar, he added. The new advisory Dietary Guidelines by the Department of Health and Human Services and Department of Agriculture recommend that people get no more than 10% of their daily calories (about 200 calories) from added sugar.

Added sugars: Adding up

While Americans are making progress in cutting sugary drinks, which make up nearly 50% of calories from added sugar—they aren't giving up some other food items with added sugar.

Refined carbohydrates and grain-based desserts, such as pastries and cookies, are a leading source of calories from added sugars. According to data from dietary surveys compiled by Popkin, consumption of refined carbohydrates has stayed about the same, and the consumption of desserts has been creeping up. Kids went from getting 297 calories a day from such sweet treats in 2003 to 317 in 2012.

Trans fats: Down and out

Americans have made huge strides in improving their diet by eliminating trans fats . A recent study by Willett and his colleagues at Harvard ranked the typical U.S. diet on a scale of 0 to 110, from least to most healthy. The score rose from 40 in 1999 to 47 in 2010, almost entirely because of reductions in trans fats as well as sugar-sweetened beverages.

The drop in trans fats "was mostly due to changes in the manufacturing process, not that people were really changing what they were eating," Willett said. Even before policies were in place to limit trans fats, and the FDA banned them , many manufacturers voluntarily started phasing them out, he added.

Instead of trans fats, a lot of food manufacturers now use vegetable oil, and dietary surveys reflect a rise in the consumption of these unsaturated fats along with the drop in trans fats, Willett said. Although vegetable oil is not necessarily lower in calories than trans fats, studies suggest this type of unsaturated fat could have health benefits whereas trans fats have been associated with higher rates of heart disease, diabetes and other conditions.

Fruits and veggies: Still not enough

From a glass-is-half-full perspective, the consumption of fruits and veggies is on the rise. American children consumed 63 calories of produce a day in 2012, up from 47 calories in 2003, according to Popkin's data. There was a similar uptick among adults.

However, experts say the increase is underwhelming. "We are talking trivial. Ten to 15 extra calories is a percent of what people eat," Popkin said. The USDA recommends two to four servings of fruits and three to five servings of veggies a day . Given that most produce is low in calories -- between 20 and 200 a serving -- the current average intake puts most Americans far below the recommended number of servings.

Increasing our intake of fruits and veggies could play an important part in improving the U.S. diet. "We have got all the mileage we can out of [cutting] trans fats, but there is huge potential for increasing whole grains and fruits and vegetables and we could gain a lot by cutting back more in red meat," Willett said.

Fast foods: Practically no difference

Despite all the reports of fast food's ill effects on health , Americans have only been slightly scaling back their intake. The proportion of calories that adults get from fast food every day dropped from 12.8% in 2003 to 11.3% in 2010. Among children, the number of average calories a day dropped from 370 in 2003 to 360 in 2012. However, the percentage of daily calories that this represents actually rose from 16% to almost 18%.

A study by Drewnowski and his colleague Colin D. Rehm looked at the types of fast food that American children are eating . The most commonly consumed items were burgers and pizzas, followed far behind by foods such as sandwiches and Mexican food. However, as Drewnowski pointed out, it does not matter that much where fast food calories are coming from. Pizza is high in salt, but "sandwiches are also sometimes loaded with sodium because of all the processed meats and cheeses," he said.

Nuts: Going nuts

Americans may be changing the kinds of calories they get from snacks. Grain-based desserts such as cookies appear to be waning in popularity, while nuts are taking off, Drewnowski said. Almonds, in particular, are on the rise.

Even though the switch does not necessarily reduce calories, it could carry a lot of other health benefits. "Essentially if you have nuts, including almonds, as snacks, that means no added sugar and much more protein and fiber and a little fat," according to Drewnowski.

Eating at home: It's still where we get our calories

Like lava lamps and tie-dye, home cooking may never be as popular as it was in the 1960s. But it still delivers a large portion of the calories we consume. A study by Popkin and his colleagues found that the number of calories that Americans got from foods cooked at home or ready-to-eat groceries eaten at home decreased from 95% in 1965 to 68% in 1996. However, the decline leveled off after the mid-1990s. Similarly, while the amount of time spent cooking decreased between 1965 and 1992, it has plateaued since the mid-1990s.

Because most calories are still consumed at home, Popkins and the other authors of the study said that the Americans could have a better diet if there were more healthy, easy-to-prepare meals. "Unfortunately, eating at home is all too often putting something in the microwave" that has a lot of calories and sodium, Willett said.