Early Friday morning, a sharply divided Supreme Court ruled that Alabama could execute Christopher Lee Price. In dissent, Justice Stephen Breyer took an unusual step: he criticised his colleagues for not meeting in person before resolving the appeal, which had been filed late Thursday night.

Generally, the justices are extremely secretive about the workings of the court. But not here. Breyer and his three progressive colleagues made the conscious decision to peel back the curtain, and in the process, cast doubt on the majority’s decision-making process.

Tensions on the post-Kennedy Court are now spilling into view. Maybe we can mediate. My recommendation: conservatives should agree to a three-day delay to handle last-minute capital punishment appeals; liberals should resist the urge to go public. The court, and the country, would be better for it.

Every year, the Supreme Court decides about 80 cases. Some take a year from start to finish. Most death penalty appeals, however, are resolved in hours, not months. Consider Dunn v Price. The prisoner was scheduled to be executed before midnight on April 11. Earlier that day, a district court judge put the execution on hold for 60 days. She found that Alabama’s proposed execution protocol would likely be more painful than an alternative method, known as nitrogen hypoxia. The state appealed. Several hours later, the Court of Appeals declined to disturb the lower court’s ruling, given the looming deadline.

At about 9pm Thursday, the state filed an emergency motion with the Supreme Court. Early Friday morning, five justices voted to authorise the execution: Chief Justice John Roberts and justices Clarence Thomas, Samuel Alito, Brett Kavanaugh and Neil Gorsuch. In a single paragraph, the majority suggested that Price waited too long to pursue his claim. This order on the court’s so-called shadow docket allowed the justices to quickly and quietly resolve a controversial matter. Or at least that was the plan.

But in response, Breyer wrote an impassioned dissent, joined by justices Ruth Bader Ginsburg, Sonia Sotomayor and Elena Kagan. He shined light on the shadow docket and explained the justices’ late-night deliberations. Breyer “requested that the court take no action until” its regularly scheduled conference on Friday. He said the “delay was warranted” so the justices could hash out the issue in person. His conservative colleagues disagreed. They wouldn’t wait a few more hours, even though Alabama had already called off the execution. (Once midnight struck, the state’s death warrant had expired.)

It is very rare for the justices to detail their internal procedures. Why did Breyer break the code of silence? It was most likely an act of despair. We are now living in the post-Kennedy Court. Various issues seem to divide the conservative members of the court. But on the death penalty, they are united.

Look no farther than Bucklew v Precythe. This 5-4 decision held that Missouri’s lethal injection protocol was not “cruel and unusual punishment”. Moreover, Gorsuch’s majority opinion explained, the courts should be sceptical of “11th-hour stays” of executions that “interpose unjustified delay”. Sotomayor, in dissent, wrote that reviewing capital cases with “an especially jaundiced eye ... would effect a radical reinvention of established law”.

Breyer and his colleagues can see the writing on the wall. At some point, the court will institutionalise Gorsuch’s “jaundiced” review of capital appeals. And going forward, there will be five votes to tip the scale in favour of the state on such last-minute claims. This recognition likely nudged Breyer to criticise how his colleagues manage their internal deliberations.

This approach has both pros and cons. First, the public have been alerted to what the court does and does not do before allowing a person to be executed. It will be little comfort to Price, and death-penalty opponents more broadly, that the justices were not even willing to meet face-to-face before allowing his sentence to proceed.

There is a cost, though, to Breyer’s disclosure. Other aspects of the deliberative process that were once considered sacrosanct may become public. Trust among the justices will be eroded. Justices who publicly air their grievances can, in the words of one federal judge, “irreparably damage the already strained working relationships among the judges” and can “serve to undermine public confidence in [judges’] ability to perform our important role in American democracy”.

Breyer and his colleagues must have made a calculated decision: highlighting the method with which the court reviewed the appeal was worth the cost of diminishing collegiality on the court.

How can this logjam be resolved? Breyer proposed that the court meet in person before greenlighting the green mile. Generally, this approach is impractical, which is why I suspect the conservatives did not want to set a precedent. Between October and June, the justices conference three times a month — in total, about two dozen times a year. (They do not meet in July and August.)

This approach, if adopted consistently, could inject weeklong delays into the resolution of last-minute appeals. Moreover, the justices maintain hectic travel schedules — impromptu in-person meetings are simply impossible. Price’s appeal was an outlier: a conference was scheduled for the next day.

Perhaps there is a middle ground. As a matter of course, the court should automatically halt any executions for 72 hours — an “administrative stay”. During this time, the justices can circulate memorandums, or even convene by videoconference, to discuss the matter. If, after three days, a majority of the court still believes the execution should proceed, then the stay dissolves automatically. And any dissenting justices can prepare a dissent under less frenzied conditions.

True enough, Price’s execution warrant would have expired during this period. But he has been on death row for two decades. Another month, in the grand scheme of things, is trivial. This minimal delay would allow the members of the court, and the public, to trust the procedural, if not substantive, fairness of the process.

• Josh Blackman is a constitutional law professor at the South Texas College of Law Houston and an adjunct scholar at the Cato Institute