Rumors of Yahoo’s interest in AOL, as recently reported in Fortune, give us pause. We understand Yahoo’s proclivity to do a deal. Advertisers and investors are flocking to Google, even though Yahoo remains the top site in terms of user traffic. As a result, Yahoo’s profits have been disappointing, and its stock is down almost 35% for the year. In today’s stock-ticker-driven management environment, CEO Terry Semel faces pressure to do something dramatic, or risk being pushed aside for someone who will. The Fortune journalists subscribe to this perspective, asking how long the board will remain patient if Semel doesn’t act. Fortune lays out Yahoo’s wisest moves as buy (AOL), sell (to Microsoft), or merge (with eBay). Not doing any deal earns the derisive headline of “stay the course,” a none-too-subtle allusion to the stubborn catchphrase recently abandoned by George Bush.

The flaw in the idea of acquiring AOL is that, while AOL would give Yahoo a bigger audience, attracting eyeballs isn’t Yahoo’s problem. Yahoo’s problem is that it doesn’t turn those eyeballs into money as effectively as Google does. Google is better at matching users with relevant ads. Thus, it draws more advertisers and gets higher rates. Investors understand this. That’s why Yahoo’s stock gets hammered every time it announces another delay in its new search platform, codenamed Project Panama, which is supposed to target ads more effectively.

If Yahoo does buy AOL, it would be repeating what our research shows as a classic strategic mistake: doubling down on a bad hand. Lagging competitors often buy each other to gain scale and compete with a market leader. There’s nothing wrong with the strategy, except when scale isn’t the root of their problems. For example, Safeway bought Dominick’s and Randall’s Groceries, but adding scale did almost nothing to prepare Safeway to compete against Wal-mart. Safeway ended up writing off more than $1.7 billion. Daimler-Benz bought Chrysler for $36 billion in 1998 to get global scale. The latest rumor is that Daimler may be planning to sell Chrysler or spin it off to shareholders—and who thinks Chrysler is currently valued at anywhere near $36 billion? (GM’s market cap is currently $19.6 billion. Ford’s is $16.1 billion.)

Rather than spending $15 billion or so to acquire AOL—and the host of problems associated with switching that fallen giant from a subscription model to one based on advertising—Yahoo should focus on its core problem, because solving that problem would create plenty of upside. Conservative estimates are that $250 billion is spent on advertising annually in the U.S., with only 5% currently spent online.

So, our advice to Terry Semel is to pass on AOL and focus on making Project Panama, or its replacement, work. There’s a ton of money to be made in the search business, and it is still early in the game.