As I expected, many readers reacted heatedly to last week’s column on a proposal to reduce teacher retirement plans so that teachers who produced the best results could be paid more.

“Our pension is one of the good things about teachers’ pay packages,” one reader said. “How dare you try to steal from our retirement!!!”

“All this garbage about rewarding the ‘best’ teachers with more pay is just a way to break the teacher unions,” another said. Some suggested other ways to finance more teacher pay, such as “cut defense spending by $200 billion” or “raise the income tax on the 1%ers.”

Some readers were friendlier to the idea. They seemed willing to wait for my promised explanation in this column of how researchers at Stanford University’s Hoover Institution thought this could work.

Their proposal is in an education policy analysis, “The Unavoidable: Tomorrow’s Teacher Compensation.” It was written by Hoover economist Eric A. Hanushek, based on background papers by Maria D. Fitzpatrick, Marguerite Roza, Steven G. Rivkin, Ben Ost, Andrew Morgan and Minh Nguyen.

In my family, I am chided for my extreme optimism. My wife calls me “the Pollyanna from hell.” Astonishingly, Hanushek and company are even more hopeful than I am that the very difficult adjustments in the pension and compensation system could ever happen.

Their analysis cited research that current employees can be persuaded to take lower pensions in return for higher salaries, at very favorable terms to the government. Hanushek said a 2016 study in Washington state by Dan Goldhaber and Cyrus Grout showed when teachers were given the choice of a defined-benefit plan, such as a pension, or a partially defined-contribution plan, which employees have to pay into, those who took the latter tended to be better teachers.

Hanushek suggested that states stop pension spiking, which is letting bonuses or extra pay near retirement inflate retirement pay. States and school systems could offer larger wages to teachers in return for not letting that money affect pension sizes, he said. “It is also possible to offer end-of-career bonuses or deferred-retirement options to highly effective teachers if they agree to stay beyond normal retirement age,” he said.

Many teachers and their unions think those would be bad ideas. They are not the only barriers to making such changes.

If states and school districts are going to pay more to better teachers, they have to know how to identify them. Hanushek said teacher assessments have to go beyond student test scores to classroom observations, teacher attendance, student surveys and other methods. The districts he cited that already have pay scales based on teacher performance were in places where unions were too weak to stop them.

“Examples of sophisticated evaluation systems can be found in Washington, D.C., in its IMPACT program and in Dallas in its Teacher Excellence Initiative and Principal Excellence Initiative,” he said in an email.

Washington Teachers’ Union president Elizabeth Davis sent me a lengthy statement explaining why the union wants the IMPACT program ended but did not say whether she thought it was adopted because her union was too weak to prevent it.

Hanushek also praised the evaluation system in New Mexico. He said the District, Dallas and New Mexico have shown gains for children from low-income families when teachers who were rated effective were given bonuses to teach low-performing students.

The federal government, under the bipartisan Every Student Succeeds Act, has ceded most of its power over schools to the states. Places such as Texas, where some of the nation’s most successful charter school networks were born, have the best chance to reform the compensation and pension systems. Even if they can’t go that far, Hanushek suggested, they can at least give localities a chance to do so.

Tennessee, he said, “gave districts considerable flexibility in determining exact evaluation-compensation packages to employ. Districts responded with innovative compensation plans” and saw achievement gains.

On the last page of the analysis, Hanushek admitted “altering personnel policies and adjusting compensation patterns have historically proved difficult, as considerable inertia exists in schools.” Yet the importance of making changes is “enormous,” he said.

When I started writing about schools, I never imagined anything like public charter schools or private school vouchers. Surprises are possible, but as Hanushek indicated, they are unlikely to appear soon in very many states.