A major provider of mortgage data said this week that the percentage of “underwater” homeowners — people who owe more than their homes are worth — is significantly lower than the company previously reported.

First American CoreLogic said it changed its methodology to take into account two things that its data hadn’t reflected: how much of a loan’s principal has been paid down and how much of a home equity line of credit is actually being used.

The result: The owners of 23 percent of all mortgaged residential properties had negative equity in their homes in the third quarter. That’s far below the 33.8 percent that would have appeared to be upside down on their loans using the old formula, CoreLogic said. Under the old method, 32.2 percent were underwater in the second quarter.

The corrections may cause some head-scratching and hand-wringing in newsrooms, at fair-lending groups and in legislative hearing rooms, where CoreLogic’s numbers have been widely cited as an indicator of the severity of the mortgage meltdown. Testimony to Congress, for example, may have been overstated.

Although the upside-down phenomenon may be less prevalent than it appeared three months ago, that doesn’t mean the revised data is comforting. To the contrary, it shows the following:

The owners of nearly 10.7 million U. S. residential properties with mortgages were underwater as of September, with an additional 2.3 million homeowners having equity of less than 5 percent.

Among the states, California has the fifth-largest level of negative equity, with 35 percent of homeowners upside down. CoreLogic’s flawed second-quarter report put that figure at 42 percent.

States with even higher rates of negative equity, according to this week’s report: Michigan (with 37 percent of homeowners underwater), Florida (45 percent), Arizona (48 percent) and Nevada (65 percent).