Global beverage giant Coca-Cola (NYSE:KO) continues to grow, but the advance is slowing. Considering that Coke's shares trade at a substantial premium to those of its peers, investors should be doubly cautious.

For the third quarter, total case volume ticked up 2%. Pretty good for a recession, you might think, but that figure is down from 5% growth in the year-ago period. I can understand a slump in year-over-year performance, since the brunt of the financial crisis hadn't yet hit consumers this time last year, but I find it particularly troubling that this modest increase represents half the previous quarter's gain. Meanwhile, competitor PepsiCo (NYSE:PEP) was able to boost beverage volume from the second quarter to the third.

Coke's financial results were less disconcerting. Earnings per share of $0.81 were flat year over year, but down 1% on a comparable basis (which excludes special items). Net income, meanwhile, squeaked out the tiniest gain, rising to $1.896 billion from $1.89 billion a year earlier. Unfavorable currency rates drove a 4% decline in revenue -- to $8.04 billion -- partially offset by stronger concentrate sales and improved pricing and product mix.

The most positive metric? Margins were up in the core business, as well as in the company's bottling investments. The latter group includes Coca-Cola Enterprises (NYSE:CCE) and Coca-Cola Hellenic (NYSE:CCH). Also, management is on track to deliver $500 million in productivity savings by the end of 2011, with much of that amount to be realized in 2009.

Those who've been following my coverage of the nonalcoholic-beverage industry know that I tend to favor Coca-Cola for its large international footprint. Basically, that means the company has an advantage over the likes of Hansen Natural (NASDAQ:HANS) and Dr Pepper Snapple (NYSE:DPS) when it comes to declining North American soda consumption and a potential U.S. soda tax.

But those crucial international results let me down this time around. Sure, case volume rose 4%, but that's an annual and a sequential decline. Encouragingly, Chinese and Indian consumers stepped up their thirst for Coca-Cola's products from the prior quarter, but I was looking for a broad-based gain across all markets.

For my bullish thesis on Coca-Cola to pan out, management needs to crank out international growth while at least stabilizing North American volumes. Instead, the third quarter saw weaker international results, while North American volumes worsened from a 1% slip in the second quarter to a 4% rout this time.

I'm not giving up on the company because of a single quarter, but until results turn up, investors may want to consider icing their plans to buy stock.

That's good sense more than it is running scared. Based on price-to-operating-cash-flow, Coca-Cola shares trade a bit higher than PepsiCo's stock, and at a rich premium to Dr Pepper Snapple and Nestle (OTC BB: NSRGY). Moreover, using the PEG ratio, Coca-Cola's peer-premium ranges from roughly 33% to upward of 60%.

If the market gets jittery, or if another quarter disappoints, there appears to be ample downside risk.

Wash down some related Foolishness:

Coca-Cola and PepsiCo are Motley Fool Income Investor recommendations. Coca-Cola is also an Inside Value recommendation. Hansen Natural is a Rule Breakers selection. Try any of our Foolish newsletter services free for 30 days.

Fool contributor Mike Pienciak owns shares of Coca-Cola, but he holds no beneficial interest in any other company mentioned in this article. The Fool has a disclosure policy.