We’re not surprised that a court challenge to the removal of four Confederate-themed public monuments in New Orleans didn’t pan out. The legal arguments against the city’s plans to take down the monuments were pretty thin, which is why U.S. District Judge Carl Barbier denied a temporary restraining order aimed at placing the removals on hold.

It now seems likely that the monuments will come down. But as a controversial decision to remove four fixtures of the civic landscape moves from the courthouse to the public square, city officials face a different judgment. How will posterity regard the city’s stewardship of its richly complicated and sometimes tragic past? That question obligates New Orleans and those who love it to act with thoughtful respect as the next chapter of this debate is written.

The monuments in question recognize Confederate leaders Robert E. Lee, Jefferson Davis and P.G.T. Beauregard. A fourth monument memorializes a white militia group that rebelled against the state’s biracial Reconstruction-era government. Last year, New Orleans Mayor Mitch Landrieu spearheaded an effort to remove the monuments, suggesting that their homage to the Confederacy sends the wrong message about racial tolerance. Defenders of the monuments argued that they are part of a civic history, imperfect though it may be, that needs to be remembered. Two city panels and the New Orleans City Council voted to have the monuments removed. Those votes punctuated a dispute that’s captured the attention of people across Louisiana and, indeed, the United States.

The intensity of the debate suggests the degree to which the legacy of the Civil War continues to resonate more than a century and a half after its conclusion. The deepest tragedy of that war, of course, was that fellow Americans answered their differences by trying to harm one another. And so, if the monuments are to come down, then let it be done peacefully.

City officials have said the monuments will be stored in a warehouse until plans for alternate display, such as a museum or park, can be developed. One of the charms of New Orleans — and an abiding complication — is that things tend to move slowly. But these monuments have historical significance, and they shouldn’t be placed out of sight indefinitely. They’re keys to a complicated and sometimes dark past that shouldn’t be ignored. City officials should commit to a timetable to repurposing these monuments in an appropriate historical display. The Atlanta History Center, where that city’s connection to the Civil War and slavery are explored with unflinching clarity, is a good model to keep in mind.

Plans for the monuments, as well as the question of what, if anything, will replace them, should rely on extensive citizen input, grounded in a respect for honest differences. That’s the best way to build public confidence in the result.