It was as if we were flying back in time: The tiny F-27 Luxair propjet flew over lush green hillsides, its twin engines droning dependably. Flying low over France, the lone stewardess announced it was a "meal flight" and proceeded to serve small trays of finger sandwiches. Then came the crowning touch: Coca-Cola in the original six-ounce green glass bottles.

We were on our way to the largely overlooked country of Luxembourg, at the heart of Europe but on the sidelines of that continent's tourism boom. While millions of Americans elbowed their way through the rest of Europe last summer, we chose a more tranquil approach.

Findel Airport in Luxembourg is a quiet, efficient place, where the walk from the plane is a short one, and where your luggage often beats you to the carousel.

In fact, the airport is all many Americans know about the country. For years, Luxembourg was famous as the tiny place served by Icelandic Air (now called Icelandair), once the principal cut-rate airline from New York to Europe. It was the country into which today's baby boomers flew as college students, and then scattered by bus or train to neighboring nations.

Remember the Grand Duchy of Luxembourg?

Verdant and sparsely populated, Luxembourg is, quite simply, an undiscovered jewel that offers a separate peace. Nestled between France, Germany and Belgium, it is 999 square miles in size, smaller than Rhode Island. It's a mouse that doesn't want to roar, a place given to gentle hills, a cool climate and quiet nights. It is the Europe of 20 years ago, a country where you can enjoy the proverbial bottle of wine and loaf of bread in relative privacy by just pulling off a road.

Last year, slightly more than 200,000 Americans visited Luxembourg, a fraction of the number who visited all of Europe that year. That's partly because many Americans don't know where the country is.

"It's all right with us that Americans are bad geographers," says Jean Dondelinger, Luxembourg's secretary general of the Ministry of Foreign Affairs. "But it's important for people to know what we are."

That streak of independence -- not atypical of such a small country -- is reflected in a line from Luxembourg's national anthem: "You may come from Belgium, France or Prussia -- we will show you our country, but we want to remain what we are."

"Luxembourg," says Dondelinger, "is not one of those places that is a capital for operetta. It is not one of those charming places located on a rock or in a nice valley that mints coins or postage stamps. We are a happy constitutional monarchy, an international center of politics, business and international finance. But we get very little attention in the world press. I can only surmise that happy people don't catch all the interest they sometimes deserve."

Dondelinger may be right. Try as we might, it was very hard to find something negative to say about Luxembourg. In fact, in more ways than not, the country is a charming caricature.

Luxembourg is a Renoir painting filled with flowers, storybook villages cradled next to peaceful rivers and castles sitting where castles should sit -- on the top of tidy, green hills.

The quiet capital city -- also called Luxembourg -- is centered around a deep valley, the Pe'trusse, which offers shady walks by a fast-flowing stream. Far above the valley are mammoth fortress walls that kept would-be conquerers out after the walls were built in the late 1600s. And in the city's Old Town you can still see bits of the 18-mile network of underground, fortified chambers, called casemates, that were built in the 1500s. Because the town was not ravaged by world wars, the architecture most everywhere is stunning.

One-third of this tiny country is covered with unspoiled forest. The hunting -- especially of boars -- is superb. There are two-star restaurants; hotel prices are nearly half those in cities a couple of hours away. And easily half a dozen major European cities are within striking distance. One day we lunched in Brussels, just a two-hour drive from Luxembourg. Then we dropped off our rental car and boarded the Trans-European Express for dinner that night in Paris.

There is something to be said for a country that embraces only the most positive aspects of provincialism. Luxembourg actually has a declining birth rate, virtually everyone is employed, and poverty is literally a foreign concept. The country does have a standing army, but there are only 550 soldiers. And 80 of those are in the band.

And how do you talk to the prime minister of Luxembourg? In our case, we walked unchecked to his office and simply knocked on the door. Official security consisted of two uniformed gendarmes polishing the prime minister's car in a small circular driveway outside his office.

"The beauty of this country," says the 48-year-old prime minister, Jacques Santer, "is that I can walk through the streets and greet everyone. But when you're a country of 360,000 people, it's difficult for Americans to understand Luxembourg is a sovereign state."

Sometimes, he adds, it's just plain difficult to find the place. "For us," he says, "tourism is very important, but at the same time we are trying to be prudent. We don't want too many people or hotels."

One hotel Santer did covet was the new Inter-Continental Luxembourg, a 348-room luxury facility on a wooded hillside near the city of Luxembourg. Santer saw the hotel as a lure to attract more European Economic Community offices and visitors who recognize the Inter-Continental name.

Ironically, notes Santer, some Europeans and Americans had no trouble finding Luxembourg during World War II.

"Too many people found Luxembourg," agrees foreign affairs official Dondelinger. The country is dotted with historical battlefields, graveyards and museums of World War II, marking the spots criss-crossed by American and German forces as they fought the Battle of the Bulge for control of Europe.

This summer, soldiers of a different kind attacked Europe again. Their ammunition was the almighty dollar, and reports from the battlefield portrayed gallant Americans tripping over each other in their struggle to commandeer available hotel rooms.

In Luxembourg, meanwhile, they could have enjoyed long, quiet walks through the park-like center of the capital city. Or they could have strolled along the Promenade de la Corniche, which overlooks the Old Town, where the city's bistros, artists' haunts and gourmet restaurants are centered. And outside the city, they could have discovered a range of adventures just by taking a 15-minute drive in any direction.

To the southeast is Mondorf-les-Bains, a spa city that also boasts a gambling spot called Casino 2000. Smallish, the casino has only two blackjack tables, five roulette wheels and a room of slot machines. The betting is rather modest, and a local joke is that the casino is named for the year in which someone will finally win something big.

To the northeast, on the Luxembourg-West German border, you'll find Echternach, a medieval picture-postcard village that has been wonderfully restored. Nearby is Vianden, on the Our River. A wonderful, perched castle guards the village in the valley. Take lunch at the Hotel Heintz, run by the same family for four generations. Meals are events orchestrated by Madame Hansen, who doesn't hesitate to serve you herself. Along with the food comes a local history lesson, though signed pictures on the walls from, among others, Margaret Truman, Gen. George Patton and Perle Mesta tell you you're not the first to discover the Hotel Heintz.

The Moselle River is the country's border with West Germany, and its wines are justly famous worldwide. And a 90-minute drive south delivers you to the Champagne region of France.

Luxembourgers speak French and German, and most learn English in school. A little-known fact: The country has its own language, called Letzeburgesch, that is more often spoken than written.

There is hardly any crime. This summer American and Luxembourg authorities intercepted an illegal shipment of sophisticated American computer equipment about to be loaded onto the regular Aeroflot plane that touches down en route to Moscow and Havana. Normally, Soviet misbehavior is said to be more of the juvenile variety. When the Tupolev 134s and Ilyushin 62s land for refueling, their crews dash into town to buy girlie magazines and Western beer.

Luxembourgers share their prime minister's pride in their modest slice of Europe, but they don't miss the lighter side of living in a tiny country where nothing in the way of major news happens.

"We may be a quiet place," says one, "but we try to maintain our sense of values at the same time as we keep our sense of humor.

"For example," he explains, "men in this country stay faithful to their wives."

That's the sense of values. Now, for the humor part.

"But we're such a small country, that everyone knows what everyone else is doing. We have a saying: If you want to have an affair in Luxembourg . . . go to Belgium."