The idea has been tested before, from the 1940s to the 1960s, under what came to be known as the Bracero Program, named for a Spanish term for laborer who works with his arms. At its peak in the late 1950s, it provided more than 400,000 temporary work visas a year to people from Mexico, most of them employed on farms. Not coincidentally, from the mid-1950s to the mid-1960s, apprehensions of Mexicans crossing the border unlawfully — a rough measure of rises and falls in illegal immigration — plummeted to near zero.

Now a group of scholars and policy makers that includes Mr. Gutierrez; Ernesto Zedillo, a former president of Mexico; Eliseo Medina, a Mexican union leader; Silvestre Reyes, a former congressman from Texas and Border Patrol chief; and Doris Meissner, a former commissioner of the Immigration and Naturalization Service have come together to pitch a similar framework as the only viable strategy to end illegal immigration for good.

Their essential point is laid out in a “Blueprint to Regulate US-Mexico Labor Mobility,” just published by the Center for Global Development. Flows of Mexican migrants to the United States have been driven since our grandparents’ day, they note, by the supply and demand for work on either side of the border, regardless of walls and other obstacles thrown in their way.

History suggests that the United States cannot eliminate immigration of low-skilled workers. But the nation can choose what kind of low-skilled immigration it will have, legal or illegal. The former seems undoubtedly better. Legal flows can be managed to the maximum advantage of the economies and workers of Mexico and the United States. Unauthorized flows cannot.

Consider what happened in 1964, when the Labor Department ended the Bracero Program over concern that immigrant farmworkers were depressing agricultural wages. Farm wages hardly soared. Unauthorized immigration did.

Then came the next big immigration law change, during the Reagan administration in 1986. Some 28 million immigrants had arrived illegally in the United States since the end of the Bracero Program, and 23.5 million had left, leaving a net undocumented population of some 4.5 million.

After legalizing three million of them, the Immigration Control and Reform Act also tried to close the border to future flows by threatening to fine employers who hired unauthorized workers. But by 1990, more unauthorized immigrants were in the United States than had been before the change in 1986.

Critics of guest workers have a point. The Bracero Program was deeply flawed. Abuses by employers who routinely violated agreements on wages, safety, housing and the like were widespread. Workers were helpless, bound to a single employer. Though theoretically they could complain of mistreatment, in practice the procedure was useless.

Today, workers on H-2A and H-2B temporary visas, which are granted to somewhat more than 100,000 seasonal workers every year, still report many abuses.

As the Blueprint points out, though, these problems can be fixed, especially in a bilateral program managed jointly by Mexico and the United States. It proposes a long list of provisions: Employers in the United States and labor recruitment companies in Mexico would have to apply for certification from their respective governments. Immigrant workers would be protected by American labor law, free to change employers within broad sectors of the economy. Jobs and workers would be matched transparently in a public database managed by American immigration authorities.

Employers would have to pay a fee to recruit Mexican migrants, which would encourage them to hire American workers first. Part of workers’ pay would be withheld in a saving account to be drawn from after they returned to Mexico. And the visa quota for migrant workers would vary annually to fit changing labor market conditions.

These ideas do not amount to comprehensive immigration reform. The authors say nothing of what to do about 11 million undocumented immigrants living in the United States. Nor do they deal with illegal immigrants from other countries.

But they suggest that, as the number of Mexican migrants seeking work in the United States has decreased from its peak, this could be an auspicious time to bundle their proposal into a broader reform effort.

Proposing a large new program for guest workers might sound crazy in the current political environment. Just hear the roar of approval that greets Mr. Trump’s proposal for a “big and beautiful wall.” Many labor unions remain highly skeptical that the United States needs any guest workers at all. Temporary migrant workers, they argue, are devices used by employers to undercut wages.

This criticism seems off the mark, though. Opponents judge the effects of visa programs for migrant workers by comparing them with an alternative reality with no migration, rather than by comparing it with large-scale unlawful migration. “History since has given reason to question that perspective,” the Blueprint states.

“It is a difficult political lift, but we’ve tried other ways for half a century,” said Michael Clemens of the Center for Global Development, the chief writer of the Blueprint. Barring legal immigrant workers will not protect American workers. But it will ensure that illegal immigration persists.

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