Most American shoppers abroad aren't even aware that they're paying the national sales tax that European countries call value-added tax (VAT), which ranges from 4.8 percent of the purchase price of most products in Slovenia and Croatia to 20 percent in Sweden, Denmark and Hungary. Because it's not meant to be an export tax, non-resident travelers don't have to pay it on items such as clothing and gifts they buy in Europe to take home. But because it's built into the price of goods, not added at the time of purchase, you have to request a refund.

Because the reclamation process can be complicated - among other things, all countries except Ireland require a minimum purchase per store, ranging from $23 in Sweden to $305 in Switzerland and Liechtenstein - American tourists last year left behind an estimated $50 million in unclaimed tax refunds. Leisure travelers can't get a tax refund on meals, lodging, rental cars or products used abroad.

For small spenders, the routine isn't worth the trouble. You have to carry your passport when you go shopping to document that you're a tourist and get a form from each store. Then you must have it stamped by a customs official in that country (if it's not a member of the European Union) or at your final departure point from the Union, which now includes Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal, Spain, Sweden and the United Kingdom.

Some shops will run off two credit-card slips - one for the price of the purchase minus the VAT and one for the tax alone; if you get the required customs validation on your purchases so the store can prove to the government that you left the country with them, it'll process only one slip, and you won't have to pay the tax.

In cases where you're due a refund, you mail the validated forms back to each store or turn them over to any of several companies with airport booths that handle the process for a percentage of your refund. These go-betweens offer the refund via mail, charge-card credit or sometimes cash.

Note that even when they've mastered a tax-free shopping trip, U.S. citizens still must pay duty on purchases from abroad that exceed America's $400 duty-free import allowance. For details, check the Web at www.customs.treas.gov.