How's this for a tax shelter? You put up $5,000 for a $50,000 greyhound racing dog. You depreciate him and take an investment tax credit, returning you $6,000 to $11,000 in cash. So you make money on the shelter alone, regardless of whether your greyhound wins or loses races.

And how's this for an outcome?

The promoter is socked with the biggest racketeering judgment ($7.29 million) in the history of Arizona. He also pleads guilty to securities fraud and is sentenced to prison. The dogs are worth only $200 to $11,000, depending on their racing records. Some of the dogs turn out to be dead.

Investors are left barking at the moon. When audited, they lose their big tax deduction and, generally, their investment, too.

You might think that no sensible person could believe that a $50,000 greyhound could be had for only $5,000 in cash. Yet middle-income taxophobes continue to be cozened by these kinds of deals: if not dogs, then cattle, windmills, TV shows, solar panels or printmaking plates.

"An individual might represent himself as a tax preparer and point out to clients that they need to do something to shelter their income," says Leroy Johnson, director of enforcement at the Arizona Securities Commission.

At first, money might come back from the IRS -- as it did with the greyhound shelter. "So in the beginning, the promoter's promises seem to be coming true, and word-of-mouth makes the scheme pyramid," Johnson told my associate Virginia Wilson. "But people don't realize that an audit can still take place," which could cross off their tax savings and cost them penalties.

Many a phony shelter creates write-offs large enough to cancel this year's tax and the tax for three previous years, besides. To collect the money, investors claim tax refunds for those previous years.

Refunds used to be automatic, followed by possible audits later. But now, local IRS offices are trying to review all tax-refund claims as they come in. If your claim appears to be based on an abusive shelter, your refund can be frozen until the auditor arrives.

Here are the sales pitches to beware of:

*You're offered tax deductions and credits yielding tax savings larger than your original investment -- so it looks like a no-lose proposition.

But to create those write-offs, the promoter asserts that your investment is worth much more than is actually the case.

You're provided with a lot of fancy paperwork to "support" his overvaluation. But when the IRS punctures those phony appraisals -- and it probably will -- you'll lose the tax benefit you expected and probably also lose your investment.

A recent IRS bulletin listed 35 cases brought against suspect tax-shelter promoters. Twenty-three of them involved inflated valuations in equipment leasing (for energy recycling and small-business computer systems); leasing master plates to produce stamps or artwork; buying time-sharing units; buying or leasing master records, cassettes, recording tapes, computer programs and video games; and investments in a TV show, a gold-mining venture, solar units and cable-TV systems.

To the best of my knowledge, no legitimate tax shelters exist that will repay a modest investment out of tax savings alone. Anything that claims to do so probably is abusive and could get you into trouble.

*You buy investments whose tax claims are starkly false. Four shelters -- two in research and development, one in horses, one in oil and gas -- recently were clobbered for creating tax write-offs by fraudulently backdating documents.

Five others also apparently were based on phony statements: for oil and mineral properties, solar-energy packages, equipment leasing, real-estate rehabilitation and dairy cattle.

*You buy simple-minded schemes that purport to make your taxable income disappear. On the IRS's most recent list of phony-shelter cases are family trusts, false refund claims, false Schedule C tax forms and false withholding statements filed with employers.

*You're conned into thinking that the income tax is either illegal or unconstitutional, hence capable of being resisted in court. All you have to do is buy the book or buy the "legal documents" that show you how to prove your claim.

A chief spokesman for this quaint notion -- Irwin A. Schiff -- was just convicted of trying to evade $49,000 in personal taxes for 1980 through 1982, and of failing to file a corporate tax return for an insurance business. He previously spent six months in jail for failure to file personal returns.