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With the island beckoning the likes of Conan and Paris and others famous enough not to need last names, it was only a matter of time before a U.S. online travel booking site offered trips to Havana.

CheapAir.com now makes it possible to book flights between various U.S. cities and Havana.

It is just one of the latest stirrings of the recently awakened “sleeping giant” of U.S.-Cuba relations – dormant for more than half a century – after President Barack Obama and Cuba President Raul Castro announced in December the restoration of diplomatic relations between the long sworn enemies.

"Since the rule change, we have seen a surge in search volumes for travel to Cuba," CheapAir.com CEO Jeff Klee said in a statement quoted by USA Today. "Arranging flights to Cuba is a little complicated, but it's the kind of thing we're good at and our technology platform is flexible enough to make it possible."

"Our team did a great job building it out in just a few weeks' time."

Earlier this year, travel search site Kayak.com showed a variety of choices for flights and hotels to Cuba, but its users cannot book trips through it.

Cheapflights.com, another search site, noticed a spike in interest in Cuba immediately after Obama announced an easing of travel and trade restrictions.

For a few days after the announcement in December, Cuba was the fourth most searched site for Caribbean travel on Cheapflights.com, the company said in a press release.

It became a popular search item again in mid-January, after the administration released details about new trade and travel regulations, which included expanding to 12 the categories of Americans who could visit the island. It jumped to number four in the most searched Caribbean destinations, behind Puerto Rico, the Dominican Republic and Jamaica.

It has remained near the top since then, Cheapflights.com said.

“There’s an ongoing and growing interest in Cuba,” said Emily Fisher, the head of North American Communications for Cheapflights.com, to Fox News Latino. “The people who are interested in going are interested in getting a snapshot of Cuba before it changes.”

“It’s like friends of mine who went to East Berlin when the wall first came down,” Fisher said, “before it became integrated with the rest of the world, when it was untouched, unwestern culture, with no chain restaurants. To some extent, it was Communist tourism -- we went through a Cold War, and tourists could see what it was like behind the Cold War. There’s a lot of that feeling with Cuba right now.”

But while Americans are getting an appetite for traveling to the long-forbidden fruit that Cuba has been for a whole generation in the United States, the U.S. tourism industry is not quite ready to facilitate trips there, experts say.

Many trips offered still have travelers going to third countries and taking connect fights, and fares often are expensive – in the four digits.

Indeed, CheapAir.com notes on its website that many restrictions remain to traveling to Cuba, even with the many dramatic changes that are taking place.

“Travel to Cuba from the U.S.A. is only legally permitted for 12 approved reasons, and (unfortunately) hitting the beach isn't one of them,” CheapAir.com says on its site.

Travelers no longer need a special license from the U.S. Treasury Department's Office of Foreign Assets Control. But their objective for traveling to Cuba must fall within one of the categories, which include religious, cultural, educational and humanitarian.

People who have relatives in Cuba were allowed to travel there before the change in U.S.-Cuba policy, and many take charter flights from the United States.

Experts on Cuba travel generally expect that it will get easier, and less expensive, to plan trips there as demand grows and the U.S. travel industry accommodates it.

“We’ve been talking to our partners,” Fisher said, “airlines and travel agencies say it’s going to be an opportunity for them. It’s a momentous change.”