It is difficult to summon much sympathy for the C.E.O.'s of the biggest companies in the world: They are, after all, more than richly rewarded to suffer whatever slings and arrows may be fired from shareholders, regulators, customers, and the press.

One could feel sorry, however, for the chief executives of General Electric and American International Group. Sure, both are under fire because their companies have stumbled badly. Yet their companies' current woes stem in large part from decisions made by their predecessors—predecessors who won't shut up but seemingly shadow their every move and misstep with public comments.

Exorcising the ghosts of the past may be part of the reason why Jeff Immelt of General Electric has decided to put the company's appliance unit on the block.

According to several reports, G.E. has hired Goldman Sachs to prepare an auction of the unit, which accounts for about 4 percent of the company's $173 billion in annual revenue.

The Wall Street Journal reports that the appliances business could fetch between $5 billion and $8 billion. The buyer is likely to be foreign, and the New York Times says that "Asian manufacturers are expected to be particularly drawn to the division, seeking to take advantage of G.E.'s widely known brand name as they try to become global businesses."

Some analysts and investors have advocated that the company shed more units, like NBC Universal, and focus on its more profitable businesses.

Appliances are a small slice of General Electric. But selling the business would be breaking a link to the past: G.E. began in 1907 as a maker of appliances. So it is the symbolic heart of the G.E. conglomerate.

It's probably not something that Jack Welch would have done, and that is the point.  

Welch created a legacy that is impossible to follow. He gave the job of C.E.O. rock-star status and made the G.E. conglomerate an exemplary model when he retired in 2001.

It is a model that Immelt needs to break.

During Welch's tenure, the G.E. Capital unit grew to account for half of the company's revenue. It was problems in the finance business amid the credit crunch that caused General Electric to stun Wall Street with a rare miss of its earnings target.

Still, that didn't stop Welch, 72, from ranting on CNBC soon afterward that his former protégé was "getting his ass kicked."

Commenting that Immelt had a credibility problem, Welch said, "I'd get a gun out and shoot him if he doesn't make what he promised now."

At least Welch recognized quickly the damage he had done. He backtracked on CNBC the next day, saying that Immelt is "a hell of a C.E.O."

Immelt, as Welch knows, has been shedding financial assets, including the subprime plagued WMC Mortgage unit, to focus more on its industrial business.

Martin Sullivan of A.I.G.—who succeeded Hank Greenberg as chief executive after Greenberg resigned in 2005 amid investigations by the Securities and Exchange Commission and Eliot Spitzer—has fewer strategic options than Immelt.

A.I.G.'s push into credit derivatives began under Greenberg. Yet the former C.E.O., who built A.I.G. into a global insurance giant, has been sharply critical of Sullivan, his former lieutenant, saying that the company is in "crisis."

Sullivan can be faulted for not moving more quickly and more aggressively: The company for some time last year seemed to be in denial about the credit crunch. But the steps being taken now—raising capital, reducing risk, and strengthening the management ranks—are the right ones.

Greenberg, who is 82, has not suggested any strategic alternatives in his criticism. He is clearly willing to talk down the value of his main stock holding simply to score some points in public.

It's time to move on.

 (Update: An earlier version of this post referred incorrectly to Hank Greenberg's departure from A.I.G.)