(FORTUNE Magazine) – We think it's possible this management team could restore the company to a point where they could be making $4 a share down the road," said one highly regarded fund manager recently about an oft-touted "turnaround story."

"This is a textbook case of how hard it is to turn around a retailer"--that's another prominent value manager, talking about the same company, retailer J.C. Penney, on the very same day.

Kind of leaves you scratching your head. And that's a major problem with investing in fixer-uppers: Often the experts couldn't disagree more on what the future might hold. That's because these beleaguered companies frequently have to take drastic steps to revitalize their businesses. The key, says Mark Keller, a senior investment officer at A.G. Edwards, "is to be leery and understand exactly why a company got where it did." And to be patient--turnarounds can take several years and involve missteps along the way.

It's also essential to separate the "spin" inevitably surrounding these hidden value plays from what is actually happening within the company (see, for example, "Debunking Oxford"). Are the companies dithering with cost structures and laying off workers, or are they actually reconnecting with their customers and working to improve the future of their businesses? We set out to handicap some of the juiciest corporate comeback stories out there. What we found are three companies that merit a look--and three that simply don't live up to the spin. Our three picks run the gamut from a company in a softening industry that's changing its entire business model to a toy retailer that literally drove its customers out of stores and now has a convincing plan to lure them back.

But there are also some similarities. For one thing, all three companies brought on new CEOs fairly recently. Each has been there long enough to prove he's on the right track, yet not so long that all his changes for the company are reflected in the stock price. Below, we've judged our candidates' turnaround prospects and ranked them in descending order, from most credible to least. Given the hung jury on J.C. Penney, however, we decided to leave it off both lists.

Compaq (CPQ). A cheap stock, a talented manager at the helm, and real signs that Compaq isn't going to be sacrificed on the altar of cheap PCs. Sure, there's some spin here, but much of it is well deserved. This is a classic story of a company that owned its industry and then stumbled badly. A mix of mismanagement, a hard-to-integrate acquisition, and a powerful rival (Dell) meant that Compaq spent much of the late 1990s explaining away past mistakes. And some would argue that much of the turnaround has already been completed. Phase one involved bringing Michael Capellas aboard as CEO a year and a half ago. Since his tenure began, Capellas has gone a long way toward showing the Street that he can fix the company--markedly tightening inventory turns, getting out of the reseller business, and improving the balance sheet. (For more, see "Refocusing Compaq" in the fortune.com archive.)

But a look at the stock shows that investors haven't fully valued the turnaround. While nobody imagines that the company will get back to its mid-1990s growth rate, the company now trades at just 21 times 2001 earnings. Says Tim Ghriskey, manager of the Dreyfus Aggressive Value fund: "To say it's cheap is an understatement." Granted, the PC business isn't pretty these days. But with a slew of products, from handheld devices to digital audio players, the company is branching out to consumers. And Ghriskey likes the fact that "Compaq has really been at the forefront of diversifying into the server and storage areas." Even though everyone knows Dell has made substantial inroads into Compaq's core PC business, he adds that when the next corporate IT buying cycle starts (most likely at the end of this year), Compaq will get a nudge there too. The company beat earnings by 2 cents in the past quarter, and if Capellas can show the Street that it can continue to deliver financially, expect phase two of the turnaround to show a similar upside.

Toys "R" Us (TOY). Lots of growth investors might utter a collective groan at the thought of investing in a retailer attempting a turnaround. And it's true--it's notoriously hard to woo back customers once you've lost them. (This is also a company that has attempted smaller comebacks before with only middling success.) But there's a compelling argument to be made that Toys "R" Us can play it right this time. First of all, it finally has the right guy for the corner office. After two CEOs that lasted about as long as the Tickle Me Elmo craze, the company snagged veteran retailer John Eyler from FAO Schwarz. "For the first time since the problems began, they found a merchant who understood what had to change in the stores," says Bill Nygren, manager of five-star Oakmark Select fund, which is up more than 11% so far this year.

Previous comeback attempts had focused on financial tightening and operational efficiencies--in effect, attempts to mimic the success of Wal-Mart. But what Eyler realized immediately is that Toys "R" Us shoppers aren't looking for the Wal-Mart experience. The new focus is on improving inventory to make sure shelves are stocked, remodeling stores to replace the warehouse feel with a more inviting space, and better staff training. Eyler also has plans to build up the company's stable of higher-margin in-house brands in areas like stuffed animals (a strategy on which FAO Schwarz thrives). And fans are nothing short of breathless in anticipation of the huge Times Square flagship store, slated to open this summer. With a major slice of real estate and FAO Schwarz-like offerings, such as a working Ferris wheel and a Lego skyline of New York City, the hope is that tourists will get a reinvigorated view of the brand.

The stock has begun to climb steadily this year after the company reported strong holiday sales. But Nygren thinks the company could earn $2 a share next year (well above consensus estimates), even assuming that both margins and sales per square foot are below their historical range. In other words, there's even more chance for upside going forward.

Conseco (CNC). In terms of the spin cycle, we'll be frank: This is definitely in "heavily soiled" territory. But the bottom line is that while the insurance and finance company may still be troubled, a talented new CEO is streamlining Conseco's business and making an awfully good case for the stock. First a brief history: This is a company that nine months ago was trading at what one fund manager called "going-out-of-business levels." Basically, its former management made a cash-burning acquisition in the home-finance segment that nearly drove it into the ground. But last June, Conseco lured Gary Wendt, formerly of GE Capital, to fix the mess. Since then he's taken a hatchet to the portfolio, raising almost $2 billion in asset sales, and has fought to improve its financial-strength rating.

Make no mistake about it: Not everyone thinks the future is so bright. Seven of the eight analysts who cover the stock rate it a hold (the other has a moderate buy). In the fourth quarter of 2000, reported in February, the company easily topped analysts' estimates by 4 cents, but some raised concerns about past-due loan numbers. Also, special charges taken during the quarter more than erased those profits. (Conseco maintains that this is a good thing, since it takes care of nearly all of the "hangover issues" left by the departed management.) Add that to fears about the slowing economy, and it's easy to see why the stock is languishing far below its trading levels of 1997 and 1998. "Some people don't totally believe that this is all fixed and that this is any kind of a growth business going forward," says Jeff Bernstein, who manages several ING Pilgrim funds. He disagrees. For starters, Conseco has about a third of the manufactured-home financing market, an industry that's experiencing major consolidation. When all is said and done, says Bernstein, "Conseco could be the 500-pound gorilla of this business."

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