Calls are growing for the Obama administration to end the decades-long practice of allowing Cubans who make it onto U.S. soil to stay here.

The practice, which stems from the 1966 Cuban Adjustment Act and is informally known as the “wet-foot-dry-foot” policy, allows Cubans who make it to the United States to remain her legally.

They can obtain permanent U.S. residency after a year and a day.

The policy has been controversial for a long time, drawing criticism from some who view it as preferential treatment. Haitian-American groups, for instance, often contrast how much harder it is for their compatriots to get legal residency in the United States.

Now that Cuba and the United States are re-establishing diplomatic relations and recently announced that embassies would be reopened in Havana and Washington, D.C., before the end of July, many argue that it’s time to repeal the Cuban Adjustment Act.

“The politics of the issue have evolved,” Marc R. Rosenblum, deputy director of the U.S. immigration policy program at the Migration Policy Institute, told Fox News Latino.

There also have been published reports about how some Cubans obtain refugee status – presumably because they fear persecution in their native homeland – yet regularly travel between the U.S. and the communist nation after obtaining legal residency here.

“People see certain Cubans abuse the Cuban Adjustment Act, and travel back and forth, taking advantage of that privileged status.”

The Obama administration, mindful of the emotionally-charged debate around the special program – Cuban exiles have pushed hard to keep it in place – quickly noted after announcing the push to normalize relations that the wet-foot-dry-foot policy would remain in place.

Remberto Perez, vice president of the Cuban American National Foundation, one of the nation’s most influential Cuban exile lobbying groups, says the re-establishment of diplomatic relations has not meant an end to the human rights abuses that have driven many to flee to the United States.

“It’s still a brutal dictatorship, and if people are risking their lives to escape the regime, we should give them asylum,” Perez, a New Jersey businessman, told FNL. “Cuba is just giving lip service and window-dressing. Cuba cannot be compared with Haiti. Cuba is a police state.”

Rep. Carlos Curbelo, a Miami Republican and the son of Cuban exiles, has drafted legislation that seeks to modify the Cuban Adjustment Act.

Among other things, his measure requires people who want to stay in the United States via the Cuban Adjustment Act to prove they face political persecution.

It would also rescind the residency of refugees who return to Cuba before they complete the process of becoming a naturalized U.S. citizen.

"When you do talk to other members of Congress about the abuses of the Cuban Adjustment Act," Curbelo's chief of staff, Roy Schultheis, told the Sun Sentinel, "everyone accepts that they exist."

Some groups, such as the Federation for American Immigration Reform, or FAIR, want to see more than just a tweaking of the Cuban Adjustment Act.

"With the re-establishment of full diplomatic relations with Cuba, our outdated Cold War immigration policies with that nation must end," Dan Stein, FAIR's president, told FNL.

"If we are treating Cuba like virtually every other nation on earth in terms of trade, cultural exchanges and diplomacy, then we should also treat Cuban citizens like everyone else when it comes to immigration to the United States,” he added.

Former Cuban political prisoner Luis Israel Abreu, a New Jersey resident who long has been active in pushing for democratic reforms on the island, says the practice should remain, although with some tweaking.

“Cuba does have conditions that are unparalleled in much of the world,” Abreu told Fox News Latino. “There continue to be dire human rights violations by the government, there continue to be people imprisoned merely for their political beliefs. Cuba is a state sponsor of terrorism, and it is led by a brutal dictatorship.”

What could change about the policy, Abreu said, is tightening the screening for who gets to stay in order to make sure the policy provides relief to people who truly are fleeing persecution, not to those who are leaving for purely economic reasons.

Rosenblum of the Migration Policy Institute says it’s hard to continue to justify a blanket granting of U.S. residency to every Cuban who makes it ashore when no other group in the world gets the same privilege.

He said the double standard is particularly glaring given the efforts by the U.S. government to deport unaccompanied minors from Central America who arrived at the U.S. border in recent years, trying flee the soaring violence and poverty in their homelands.

“They’re treated very differently,” Rosenblum said.

He added that the Cuban Adjustment Act can be applied more fairly without doing away with it.
Rosenblum said the act does not require the U.S. to give every Cuban reaching the U.S. a path to refugee or asylum status.

“It authorizes [the U.S.] to grant a visa to arriving Cubans, but doesn’t require that it be given to everyone who arrives here,” he said. “But that is how it has been implemented. It shouldn’t be a blank check.”

Elizabeth Llorente is Senior Reporter for FoxNews.com, and can be reached at Elizabeth.Llorente@Foxnews.com. Follow her on https://twitter.com/Liz_Llorente