Whether you figure your own federal income tax or have an accountant do it, you may need it calculated twice. Once is for regular tax. The second calculation – if you don’t make it, the government will – comes up with a figure called the alternative minimum tax. You pay whichever is larger, and it may come as a nasty shock. Besides, just figuring the alternative tax can take up an additional 12 hours of paperwork.

This add-on mainly hits the well-to-do, but it is so complicated that even a person with a modest income can be caught in it. And even professional tax advisers have a hard time explaining or predicting its impact.

Here is how it works: The traditional calculation lists all the permitted exemptions and deductions and tax breaks like home mortgages and home equity loans, child tax credits, charity contributions, qualified retirement accounts and state and local taxes. The second calculation uses a different set of rules. It strips off most of the tax breaks except mortgage interest and cash contributions to charities. Then it provides a somewhat larger personal exemption and applies a slightly lower tax rate for your bracket.

How did this thing get started? Then-Treasury Secretary Joseph Barr caused a sensation in 1969 by holding up a list of 155 Americans who had earned more than $200,000 and paid no federal income tax. Congress reacted to the ensuing uproar by creating the alternative minimum tax in late 1969. It was intended to catch rich tax avoiders.

Two problems: Congress provided no adjustment for inflation. And it mostly neglected the issue year after year, despite rising public complaint.

As a result, the alternative tax has been creeping down the income scale. Some tax consultants advise making the calculation if household income is $75,000 or more. Others put the threshold at $50,000. Others say they don’t know without doing the arithmetic for a given taxpayer. Government statisticians say about 3 million households will be hit by the extra tax this year. They say that in 2005 the number could rise to 11.3 million and by 2010 to 35 million households, or one-third of the public.

This ballooning super tax is tough not only on some not-so-rich individuals but also on the economy as a whole. By taking away the tax break from contributing to an Individual Retirement Account or a 401(k), it depresses the national savings rate. By penalizing home equity loans, it slows spending that eases recessions and promotes recovery.

The Tax Policy Center, an independent think tank, has said that the alternative tax “must be reformed, if not eliminated but fixing [it] will be expensive.” Even the Internal Revenue Service has serious reservations about the tax. Nina Olson, the IRS’s national taxpayer advocate, told a CBS Evening News interviewer, “It’s a horrible provision. We are really sorry about the impact of this tax, but it is not for us to rewrite the laws; it’s for Congress to act.”

Aside from minor tweaking, congressional action seems unlikely, especially in a time of budget deficits. Well-placed complaints might help, but the cleanest solution, complete repeal of the extra tax, would cost the U.S. Treasury $1 trillion over the next 10 years, according to the National Tax Journal. Incremental reform is the most the nation may be able to afford.