In early February, U.S. Federal Reserve chairman Alan Greenspan noted that overheating of the U.S. economy was beginning to generate upward pressure on wages through low unemployment. One way to counter that source of inflationary risk, he suggested, was by significantly increasing legal immigration from abroad–whether the immigrants be high-tech Indians or low-wage Mexicans. Greenspan clearly would prefer to limit any opening of the immigration door to the current business cycle, and to regions and sectors of the U.S. economy directly affected by the low unemployment rates. But he is visionary enough to see that the U.S. employment problem will outlast the current boom, and that any solution needs to be for the long term.

More surprisingly, on Feb. 16 in New Orleans, John Sweeney and U.S. labor unions in his AFL-CIO made statements that have changed the nature of the game. The unions started by acknowledging that “the current system of immigration enforcement is broken.” True, not exactly a Nobel Prize-winning discovery, but a startling declaration from one of the bulwarks of previous immigration policy. The unions went on to recognize that “undocumented workers and their families make enormous contributions to their communities and workplaces, and should be provided permanent legal status through a new amnesty program; regulated legal immigration is better than unregulated illegal immigration.”

Granted, the AFL-CIO said it was “troubled” by guest-worker programs, and placed some limits on the type of immigrants eligible for any new amnesty. Nonetheless, the two declarations of principle open a splendid window of opportunity for countries ranging from Colombia and El Salvador to Mexico and the Dominican Republic. Latin nations can now call for negotiations with the United States on a much broader canvas than in the past. Mexico, for example, could take advantage of NAFTA and begin to work on the liberalization of a key international, globalized flow of today: that of labor.

A free-labor agreement covering Mexican, Central American and the Caribbean could look something like this. The first step would be an amnesty program for undocumented workers who are currently in the United States, and who could somehow show their more-or-less permanent status. Those workers constantly migrating to and fro would be dealt with separately. This is consistent with precedent; the history of U.S. immigration policy is studded with amnesties. And it would end the silly notion that by making life miserable for undocumented foreigners, they might simply throw up their hands and go home.

Second, a new agreement could provide for a negotiated, significant increase in the number of permanent working permits or visas extended to Mexicans and other Latin Americans. In the case of Mexico, new estimates by the Mexican Population Council show a net annual outflow–both legal and illegal–of nearly 300,000 emigrants; new, nonamnesty visas issued to Mexicans amount to about 65,000 per year. It is obvious both that the United States could issue more visas and that Mexico could use them.

The third item would involve the regulation and administration of all existing or new, to-be-negotiated sectoral, regional and seasonal agreements, often referred to as guest-worker programs. There are many precedents for this elsewhere in the world. And there is every reason to believe that hundreds of thousands of Mexicans, Salvadorans, Dominicans and Peruvians would prefer to travel north for a specific period of time, for a specific job, with predetermined, fair pay, and repeat the experience every year, than to be deprived of this opportunity or exchange it for an undocumented, dangerous and underpaid adventure. There are good and bad previous examples of such arrangements; their joint administration would help ensure that the virtuous models were followed and poor ones discarded.

If the United States believed that this type of negotiation was in its own interest, it would ask nothing from Mexico and the other countries in exchange. On the other hand, those countries that generate immigrants could offer–though this would be too delicate–to share the responsibility for regulating the flow of undocumented workers. Between what the United States would want (which is for Mexico to seal off its own borders) and what Mexico would prefer (which is to do nothing to regulate a persistent flow of undocumented workers) there is ample room for compromise. All Mexico, the other Latin American countries and Washington need are imagination, boldness and generosity. Yes, that’s a tall order. The alternative, however, is to continue with a system that is manifestly broken, and needs to be fixed.