Richard Parsons, Time Warner's CEO, exudes warmth. That quality helped stabilize the company after its ill-fated merger with AOL. But at the annual Sun Valley gathering held by investment banker Herbert Allen in July, Parsons got a cool reception from one of his biggest shareholders. The masters of the media universe passed the days golfing, hiking and fly-fishing, and mixed in sessions on the future of digital media. There were private meetings, too, including one between Parsons and fund manager Gordon Crawford of Capital Research Group, Time Warner's largest investor, according to a senior Time Warner executive. Crawford, by this account, had blistering comments about the stalled stock price, frozen in the midteens for roughly two years (Parsons arranged a briefing for him by Time Warner co-chairman Jeff Bewkes; Crawford wouldn't comment). Parsons also spent time under the Idaho sun with Aviv Nevo, a press-shy man who is also a big shareholder. Nevo has been visiting New York headquarters more often, and has grown vocal about his concerns. Nevo couldn't be reached for comment.

But it now seems those two were just warm-up acts. Last week Parsons awoke to headlines about a very public campaign by billionaire Carl Icahn. Icahn, who owns 5 million Time Warner shares, uses the muscle of his $2 billion hedge fund to pressure underperforming companies. He is expected soon to outline his plans in a regulatory filing. He reportedly wants Time Warner to increase the size of its planned offering to sell a stake in Time Warner Cable to the public. He may also push Time Warner to buy back more stock, or lobby for a sale of AOL or Time Inc. Icahn didn't respond to messages left at his office.

For five years, Time Warner has been a neck-wrenching ride for investors--from the dreams inspired by its $350 billion merger with AOL to the bursting tech bubble, and accounting scandals and culture clashes that crushed its stock price and wiped out $200 billion in shareholder wealth. Parsons, a politically astute insider who was tapped for the CEO job in May 2002, faced a tough task: put the company's rough recent past behind it by settling federal investigations and private litigation over its accounting, and get the warring AOL and Time Warner factions working together. He's largely delivered. He's also cut debt, and sold off Warner Music. Two weeks ago the last lawsuits were settled for $3 billion. He is commencing a $5 billion stock buyback. But the shares have remained leaden. Time Warner has argued that many media companies are struggling with undervalued shares and growth issues. Yet this month Merrill Lynch analyst Jessica Reiff singled out Time Warner, cutting her rating on the company to "neutral" from "buy." A big factor: "We see few catalysts for the stock over coming months."

For now, Parsons seems intent on staying the course, betting that investors will begin to see a payoff later this year. A radical shift in strategy wasn't necessary, he said in a recent CNBC interview. The comment suggests he could enhance the steps he's already planned--for instance, increase the share buyback and the offering in Time Warner Cable. But his remarks also suggest he wouldn't, for instance, favor selling Time Inc. After all, it's a big part of Time Warner's DNA, doesn't require lavish investments and produces a gusher of cash.

Parsons still must decide the fate of AOL, which has struggled since the merger. Its latest strategy is to move to an advertiser-supported portal from its subscription-based model. AOL has seen a sharp jump in advertising revenues, but its base of subscribers for dial-up connections is eroding as customers embrace broadband. Time Warner has studied a sale of AOL, but Parsons seems inclined lately to wait and gauge the prospects of the new strategy.

Still, Parsons will get to rethink these matters at a looming top-level meeting. He is reviewing the company's strategy in September in a session with his top executives and division heads, and is expected to later brief the board. It will be a particularly sensitive time for the directors. All boards are under greater scrutiny in this era of tougher corporate governance, and Icahn has been known to use lawsuits to make his case against companies for changes. The pressures could exaggerate a natural fault line on the Time Warner board. They're hardly a cohensive bunch. The always-volatile Ted Turner, who sold his CNN cable network to Time Warner, is especially bitter over his experience with the media giant. Turner publicly called for the breakup of all large media companies last summer in a Washington Monthly article titled "My Beef With Big Media." It's unclear whether Turner, who has sold huge chunks of his Time Warner stake in recent years, intends to stick around. Recent press reports say he plans to resign from the board.

Turner's fellow directors include AOL founder Steve Case, who's a much-maligned figure throughout Time War-ner. Case was stripped of his post as Time Warner chairman in a shareholder backlash led by Crawford. And Parsons dropped "AOL" from the Time Warner name. Many have speculated that Case might be interested in trying to reacquire AOL, though Case himself hasn't discussed it publicly.

Parsons's future seems very secure, however. By all accounts, he has the board's support. But top industry execs and bankers say he has one noteworthy detractor: Crawford, who apparently doesn't believe Parsons is the right leader for the long term. He's been trimming Capital Research's holdings in Time Warner, and is widely known to have soured on the entire media sector. Still, the executive lineup could be in for a change. Last week reported that Bewkes, the co-chairman, could be named president in 12 to 18 months, presumably following the retirement of co-chairman Don Logan. But promoting the former HBO wunderkind alone may not win over Crawford and other investors. A little heat from a rising stock price would help.