NEW YORK (CNN/Money) – Many who say Social Security is in crisis suggest overhauling the system by partially privatizing it, allowing workers to invest some of their Social Security taxes in personal investment accounts.

But even proponents of privatization acknowledge that personal accounts alone won't resolve Social Security's long-term solvency issues. Rather, changing the way initial benefits are calculated could. And that's a feature of key reform proposals that promote personal investment accounts.

"Personal accounts are neither necessary nor sufficient," said Olivia Mitchell, a professor at the University of Pennsylvania's Wharton School, who served on both the President's Commission to Strengthen Social Security and the Congressional Budget Office's advisory board on Social Security.

And in a private White House memo published in the "Wall Street Journal" on Thursday, President Bush's director of strategic initiatives, Peter Wehner, wrote: "We simply cannot solve the Social Security problem with Personal Retirement Accounts alone. If the goal is permanent solvency and sustainability ... then Personal Retirement Accounts ... are insufficient to the task."

That may be why President Bush, who is making a heavy push for privatization, is reportedly leaning towards changing the formula by which initial Social Security benefits are determined. That idea is a major feature of "Plan 2," the leading privatization proposal put forth in 2001 by the President's Commission to Strengthen Social Security.

Here's the crux of the proposed change: Instead of linking -- or indexing, as it is known -- initial Social Security benefits to wage growth, the starting benefits would be indexed to inflation. Since inflation tends to rise less quickly than wages, it's a reduced measure by which to set starting benefits.

It's that formula change that would bring the system into actuarial balance, but it also would result in a cut in future retirees' benefits.

"The proposed switch from wage to price indexing under Plan 2 would reduce benefits relative to current law," according to a report by the Congressional Budget Office (CBO).

Here's an example of how a change in indexing under Plan 2 may reduce future retirees' benefits, even after taking into account the gains of a personal investment account:

The CBO estimates that when a worker earning the median income born in 1990 retires, he would receive $14,500 a year in today's dollars. That includes the money he'd draw from his personal investment account – assuming a 4.9 percent annual return -- and his Social Security benefits.

Under the current system, that worker is promised a benefit of $23,300. But even critics of privatization acknowledge that the current promise can't be met since the system won't be taking in enough revenue when he retires to pay out all its obligations.

But even if the system only paid out what it could afford to -- about 80 percent of the current promise -- the worker in this example would receive $18,100, which is $3,600 more than he'd get under Plan 2.

Still, proponents of privatization point to other benefits of personal accounts. "There is a value above and beyond the expected dollars," Mitchell said.

For example, Mitchell explained, one might argue that it is less risky to have a personal investment account in which one can diversify and own one's investments rather than to rely solely on a pay-as-you-go system in which your Social Security benefits are "entirely reliant on the willingness and ability of the next generation to pay those taxes."

Under Plan 2, creating a personal investment account would be voluntary and only a portion of your Social Security payroll taxes could be invested in it.

Also, Mitchell noted, for those workers who never make it to retirement, Plan 2 would allow them to leave the money in their accounts to their heirs.

And having personal accounts in combination with a change to price indexing is expected to give future retirees a higher benefit than they'd receive if only price indexing were adopted. "Individual accounts offset some of the benefit reduction you'd otherwise see," said Michael Tanner, director of health and welfare studies at the libertarian Cato Institute.

Whatever changes are made to Social Security, President Bush has made clear that the benefit levels of current and near retirees would not be affected, although he has not specified what ages define "near" retirees.