NEW YORK (FORTUNE) - Jeffrey Immelt took over as CEO of General Electric three days before 9/11, and since then he has labored to shed the company's insurance businesses, whose volatility and commodity characteristics he doesn't think fit GE.

In mid-November he announced the offloading of his major remaining headache: the company's large, money-losing property-and-casualty reinsurance operation, lodged in the optimistically misnamed GE Insurance Solutions.

"If you see the smile on my face," Immelt told Wall Street analysts, "you will know how I feel about this deal."

He then went through a dictionary of downbeat language intended to describe his relief at getting this monkey off his back. Insurance, he said, had been a "real burden" for GE, a business that "slowed down our growth."

Well, yes, all of that -- and also a business made to order for managing earnings, in a company long accused of doing so.

Property and casualty insurance companies have to estimate their future claim costs every year, and if they underestimate these -- either intentionally or ineptly -- the result is overstated profits. GE's new insurance deal seems likely to require the company to own up to big cost underestimates in the past.

Before GE sells its reinsurance operation to Swiss Re for $6.8 billion, the contract requires GE -- that is, except for a couple of qualifications that may or may not turn out to mean a lot -- to add $3.4 billion to its reserves for future claims costs. In this year's books, that will be the main cause of an after-tax $3 billion loss for insurance at GE.

The hard fact is, any additions to reserves are a cost that should have been matched to premiums recorded in earlier years or the first three quarters of 2005. So if GE were to actually put up the full $3.4 billion, it would be acknowledging -- implicitly -- that its costs were hugely understated in the past and its profits overstated.

Both Swiss Re and GE have said that most of the reserves are likely to be assigned to pre-2001 years. That would mean the overstated profits occurred on former CEO Jack Welch's watch. The $3.4 billion in reserves, if applied to GE's four best insurance years, 1996-99, would undo more than 90 percent of the insurance earnings that GE reported for that period. (Welch declined to comment.)

The really interesting question is whether GE will add the full $3.4 billion to reserves, or will try to squeeze by with a lower figure that would look more presentable. The $3.4 billion and the reserve stipulation were the result, says vice chairman Dennis Dammerman, GE's point man on the deal, of "negotiating, negotiating, negotiating." Swiss Re was almost "paranoid," says Dammerman, about wanting to be fully reserved, and GE, above all, just wanted out of this infernal business. GE agreed to add the $3.4 billion to reserves, he says, provided accounting rules and the judgments of its actuaries find that much appropriate. If not, then GE will take the rest of the hit elsewhere in its income statement.

That's GE's thinking. But a Swiss Re spokesman sees it differently. "There is no dispute between us and them," he says, "that $3.4 billion in reserves is required." Perhaps Immelt's insurance troubles aren't behind him quite yet, after all.