The Coca-Cola Company (NYSE:KO), the world’s largest soft drinks business, is expected to boost third-quarter profits despite lagging sales, as it cuts costs and markets heavily, and rebounds partly from a terrible second quarter.

The company continues to rely on non-U.S. markets for growth, as obesity fears and a long-term decline in soft drink-sales burden its American market.

Coke, which is based in Atlanta, Ga., reports earnings on Tuesday, before the market opens. Analysts polled by Thomson Reuters expect a modest 6.3 percent uptick in earnings per share, to 53 cents per share. Revenue is expected to slip by 2.3 percent to $12 billion, though net income should grow from $2.33 billion a year ago to $2.41 billion. 

The modest growth expectations for the third quarter follow an unhappy second quarter, where global sales volume grew only 1 percent, the lowest for Coke in 10 years, according to Citigroup Inc. (NYSE:C) analysts.

Even as the company blamed unusually wet weather and a tough economic environment, including social unrest in Brazil and the Middle East, many investors stay wary about third quarter results, believing that interest in soft drinks has permanently slowed, wrote Citi analysts.

Sales of carbonated soft drinks, which include Coke’s flagship Coca-Cola, alongside its Fanta and Sprite brands, represent 75 percent of Coke’s global sales, they wrote.

Coke’s brand investments are also expected to start showing results, wrote Barclays PLC (LON:BARC) analysts, combating slower growth in emerging markets and a budding distaste in North America for diet as well as sweetened soft drinks.

Recent data also suggests that Coke has focused on deep holiday promotions combined with slightly higher daily pricing, which contrasts with its rival PepsiCo, Inc. (NYSE:PEP)’s cheaper ordinary prices, wrote Barclays analysts. 

S&P analysts expect the company’s operating profit growth to outpace sales growth slightly in 2013, as the company sets higher prices and cuts costs. They expect EPS boosts in the second half to beat EPS drags from the first half. 

In an industry where sales volumes are key, Coke has gained market share in some core businesses, like its sparkling, juice and tea units, said Citi analysts. Coke has concentrated heavily on orange juice recently, according to Bloomberg.

North American sales over the third quarter were probably flat compared to the year before, though results will be boosted by aggressive pricing and promotions and fair sales of non-sparkling drinks, wrote Barclays analysts. European sales have slowly recovered, Latin America sales continue to face obstacles, and Coke’s clever China marketing should see the company return to growth there.

“We expect the absolute growth rates in most geographies to improve sequentially off of very low levels in 2Q13, as the company and industry move beyond several one-time factors,” wrote Barclays analysts on Oct. 11.

Coke also relaunched in Myanmar in early June, with plans to invest $500 million over five years. That could impact earnings this quarter, though it’s unclear by how much. The company also launched its low-calorie stevia-based Coca Cola Life drink in Argentina in early June, which analysts said has fared well.

In the broader industry, one analyst cited Nielsen data showing that full calorie drink sales fell 1.7 percent in September.

Goldman Sachs (NYSE:GS) drinks analyst Judy Hong summarized the outlook well: “KO (Coke) and PEP (Pepsi) could show some sequential volume improvement from a weak 2Q. While U.S. is likely to show only a slight improvement, international growth does offer some support.”

PepsiCo, Inc. (NYSE:PEP) will report on Wednesday, a day after Coke, and is expected to face similar challenges from a sluggish North American market, though its Frito Lays food business should stem declines.