Just as U.S. policy toward Cuba has changed, so must U.S. policy toward Cubans . But the change in immigration policy, like the change in diplomatic policy, needs to proceed carefully, or it may trigger exactly the kind of crisis both countries want to avoid.

For almost half a century, Cubans have received unique treatment under U.S. immigration law. So long as they set foot on U.S. soil, Cubans are all but guaranteed admission. They can get a green card within a year and are basically exempt from deportation and immigration enforcement policies affecting other noncitizens. Plus, since they’re treated as refugees, they qualify for federal assistance and other benefits.

Yet as ties have improved between the U.S. and Cuba, some unforeseen consequences have become glaringly evident. The easing of travel restrictions by both sides has led to “refugees” who freely shuttle back and forth between the two countries. (Unlike other refugees, Cubans can travel back to their country without jeopardizing their U.S. immigration status.) Moreover, the lack of rigorous background checks has created what Florida’s Sun Sentinel calls the “Cuban Criminal Pipeline,” a burgeoning population of petty and not-so-petty crooks, many of whom fraudulently claim federal benefits.

Cubans, who live under a repressive regime that distributes poverty rather than opportunity, have good reason to emigrate. And Cuban immigrants have immeasurably enriched the U.S. But the anomalies and widespread abuses of U.S. immigration policy toward Cuba have sparked an outcry even among the most die-hard opponents of the Castros. Defending the existing policy is even harder in the face of the much higher hurdles that face those fleeing violence in Syria and Central America.

Yet changing the system comes with its own risks. Fears among Cubans of a change in policy have already triggered a near-doubling in arrivals during the 2015 fiscal year, to 43,159. Mexico and the nations of Central America are struggling with the increased flow, which has been abetted by the region’s smuggling gangs. (More than 4,000 are stuck in Costa Rica, their journey northward blocked by Nicaragua’s government.) A protracted legislative battle to repeal or rewrite the Cuban Adjustment Act, the 1966 law that codifies U.S. immigration policy toward Cuba, would send even more rushing for the exits.

President Barack Obama could use his executive authority to subject all Cubans who arrive in the U.S., by whatever means, to screening: They would have to prove they faced a credible fear of persecution in order to be paroled into the U.S. Those who were economic, rather than political, refugees would be sent back to Cuba. That change could be made relatively quickly, and might deter many Cubans from making an expensive and now more uncertain trek. Once that administrative measure is in place, Congress should then junk the Cuban Adjustment Act.

Of course, the best way to persuade Cubans to stay in Cuba would be for the U.S. Congress to drop its embargo and for President Raul Castro to speed up the opening of his country’s economy and political system. That’s the adjustment Cuba really needs.

— Bloomberg News