New York Times News ServiceThe Le Sirenuse hotel on the Amalfi Coast in Positano, Italy, is a destination worthy of seeking during a block of free time on a tour.

The brochure for Madagascar looked inviting. So did the one for Easter Island, and the one for Antarctica, too. We’d never been to any of those places.

So why did my husband, Dave, and I, independent travelers who usually prefer to rent a car and scout our own itinerary, go for an introductory tour of Italy, where we had been seven times before?

We signed onto the Smithsonian Journeys’ Highlights of Italy trip — 17 days of quick stops, from Ravello in the south up to Venice — mainly because the study leader was David Gariff, a brilliant art historian at the National Gallery of Art in Washington.

But would repeating what we had seen and done along most of its itinerary be a good way to spend time and money?

Not surprisingly, no less a European-travel expert than Rick Steves says that there’s an upside to joining a tour that retraces familiar territory.

“For me, it’s a whole new experience going back to places I know very well,” Steves told me. “There’s no pressure to see the blockbuster sights. Our guides always empower veterans to slip out and wander.”

Once we had signed up for our Smithsonian trip, we determined to personalize it. We prepped by looking back over our earlier visits to recall what we’d missed.

There would be free time to fill with strategic stops of our own, from splurge restaurants to small museums and churches that we had missed or were eager to revisit.

David Mulligan, of Johnstown, New York, a retired high school French teacher, has taken about 30 group trips with Road Scholar, the nonprofit educational group that began in 1975 as Elderhostel.

“I always do the group activity because I don’t want someone to say, ‘You missed the greatest thing,’ but then I do wander off,” Mulligan said. “When I was with Road Scholar on a tour of Northern France, a repeat for me, I went off in Auvers to explore the fields. I swear I saw the same crows van Gogh painted there!”

On the other hand, some prefer to use any free time to return to their favorites.

“I do the things I can’t imagine being in that city and not doing,” said Sharon Irving, of the San Francisco Bay Area, who has taken many repeat tours. “When we stop in Florence, my favorite city in the world, I go to San Marco to spend uninterrupted time with some particular Fra Angelico pieces, especially his ‘Last Judgment.’”

A three-day stop in Rome tailored to first-timers was a twofer for us: a chance to plug holes by seeing things we had missed in five previous visits and, just as significant, to enjoy again some of the most important sights in the world, this time with Smithsonian Journeys’ local guides and Gariff.

Veteran travelers who join repeat tours often do so for the ease of getting from one familiar spot to the next. But there’s also the advantage of sharing meals — and discoveries — with others.

Pamela Cooper, of New York, who has traveled on her own extensively, chose a tour of France even though it duplicated much of what she had seen in many stays in Paris.

“Occasionally, I had felt a need for company,” she said, “so I picked a Rick Steves tour for its free time, because I wanted people to talk to, but not all the time.”

That friendship factor was a plus for us, as well, but on Day 2 of the Smithsonian trip, while we were just getting to know our 20 new tour-group friends, we split for one special celebration. It was our third time on the Amalfi Coast, and my off-the-menu goal was a world-class dinner at the dreamy Le Sirenuse hotel in Positano that I’d had my eye on since our last trip. Before we left home, I had emailed the restaurant to find a driver to return us to our tour hotel that night.

Using email also worked well when we saw that we would have a free morning and afternoon in Rome. We booked some walks with docents offered by the U.S.-based Context Travel, which we have used in several European cities for its focused topics, skilled guides and maximum of six tourists per walk. Context and other companies such as London Walks and Paris Walks allow you to plan visits that aren’t on most highlights schedules.

We met Context docents for walks to a few lesser-known pagan, Roman and early Christian sites near the Colosseum and another of the three major churches with Caravaggios in side chapels.

Websites such as Tickitaly also work well for reserving entry to places not included on a highlights itinerary, several weeks or months before a trip, such as “The Last Supper” by Leonardo, at Santa Maria della Grazie in Milan. When we saw that we would have three free hours in Florence, we booked a tour of the Vasari Corridor, the elevated private passage the Medici built in the 1560s to connect the Palazzo Vecchio to the newer Palazzo Pitti across the Arno, which now houses much of the Uffizi Gallery’s mammoth collection of self-portraits.

Some of our finest hours weren’t during free time.

I went AWOL in Florence, where I left Dave and the group on its way to see Michelangelo’s David. Instead, I figured the better way for me to soak up a sunny Palm Sunday was to head for San Miniato al Monte, the stunning vantage point across the Arno, overlooking all of Florence. I was in time for the procession with olive branches (instead of palms) in the glorious 11th-century basilica.

I felt the thrill of exploration while walking down the hill and across the Arno, toward my other destination — the Medici Riccardi Palace, which we’d never visited. As I approached the Palazzo Vecchio, a huge crowd in the Piazza della Signoria erupted as trumpets announced a procession decked out in Renaissance costumes, heading through the square. The excitement of the moment was huge.

People who take highlights tours seem to share the view that they offer the best of all worlds: the chance to make your own discoveries, while seeing a familiar country through new eyes. The highlight of our 17 days proved the point.

Leandro Marandola, a Smithsonian tour leader, had worked his wonders. In an unscheduled stop, our bus rolled into the majestic American World War II cemetery, just south of Florence, near sunset. Marandola had persuaded the caretaker to wait for us before lowering the Stars and Stripes. As 16 of us faced 4,398 white marble crosses and Stars of David, the five military veterans in our group, including my husband, folded the flag.

We would not have had that shared moment, contemplating the magnitude of the sacrifice by American soldiers and the beauty of the cemetery, if we had not made a return trip to Italy.