Washington (CNN) Recent late-night orders , an abrupt dismissal of a case after oral arguments, and long-pending appeals that have fallen into a black hole at the Supreme Court have cast fresh scrutiny on the inner workings of America's top tribunal.

The nine justices hear arguments and issue signed rulings in about 70 cases each annual term. But that constitutes only part of their work. In an oak-paneled conference room just off the chambers of Chief Justice John Roberts , they cull through an estimated 7,000 petitions annually from people who have lost cases in lower courts. They also rule on motions to intervene in lower court proceedings, most consequentially related to scheduled executions.

In deciding what to decide, through internal rules not made public but described here, they can often influence the nation's law as much as any signed opinion.

Clashes among the justices over some of these orders, and the internal rules that guide them, have spilled out into the public sphere. Earlier this month, Justice Stephen Breyer, in a dissenting statement signed by his three fellow liberal justices , suggested that the court majority is arbitrarily applying its rules, at least in death penalty cases.

University of Chicago law professor William Baude, who has chronicled the court's "shadow docket" over the years, said Breyer's complaint underscored that when justices offer scant explanations, it is difficult to know whether they are operating fairly or unfairly.

"You reach a point when members of the court start exposing internal procedural complaints because they're so frustrated with where the court is going," Baude observed. "That can undermine the court as a court of law."

At a time when the Supreme Court is under greater scrutiny for potential partisanship, and Roberts has fought back against President Donald Trump's attacks on the judiciary, it remains difficult for the public to assess much of the court's work.

The mysteries are large and small, from ambiguous signals in capital cases to undisclosed rules governing the screening of petitions. The court does not reveal, for example, how many votes are needed when someone who has lost in a trial court seeks to bypass the usual appeals court review and go right to the justices.

Former court insiders have told CNN it takes five votes for such extraordinary review, rather than the usual four that the court states are required to grant a regular petition and hear oral arguments.

The Trump administration has sought such action in a series of cases, including in the dispute over a proposed citizenship question on the 2020 census, which the justices accepted and heard last week.

Other unknowns surround pending cases. For months the justices had declined to act in any public way on claims of workplace discrimination based on sexual orientation or transgender status, but suddenly announced in a brief order last week that they would hear, next session, a trio of long-pending LGBTQ cases

There has been no sign of action on a long-pending case from Indiana testing a law that would, among other provisions, block abortions based on the sex, race, or disability of the fetus, or on a closely watched dispute from Oregon brought by bakery owners who were fined after declining to make a wedding cake for a same-sex couple.

The justices are now in a two-week recess. They will next issue a scheduled orders list on May 13. That is also the next likely date for signed opinions. Among the high-profile cases that have been subject to hearings are those concerning a 40-foot "Peace Cross" monument on public ground in Maryland, the census lawsuit and partisan gerrymanders in North Carolina and Maryland.

The overall secrecy of the institution is reinforced by its declining to allow cameras of any type in the courtroom or to permit daily release of audiotapes from oral arguments on cases. Roberts turned down a request for same-day audio in the census case from members of the US House of Representatives and media entities such as CNN.

The room where it happens

Very little is made public about how the justices screen appeals, beyond the general rule that it takes the votes of four of the nine justices to accept a petition and schedule it for oral arguments. Insiders say that if only six or seven of the nine justices are participating because some have recused themselves from a case, three votes are enough to grant a petition.

When they decide which cases to accept or reject, the justices meet alone, with no law clerks or administrative aides.

The nine sit in black leather chairs, neatly spaced around a rectangular table. The private conference room is distinguished by a black marble fireplace and a portrait of the great Chief Justice John Marshall.

Individual justices keep track of votes and the discussion, but the real note-taking task falls to the newest justice, Brett Kavanaugh. The junior justice is responsible for providing information to the clerk of the court for the orders' list.

Votes on whether to accept or reject a case are not made public. Rather, the clerk of the court compiles for public view a long list of the rejected petitions and a short one of those to be scheduled for oral argument. Dozens of cases each session, however, fall into a limbo of sorts, with action delayed for months. Some are quietly held for resolution in potentially related disputes already accepted for court review.

Insiders say it takes four votes to hold such cases. No public notice is made regarding those actions. However, if the court postpones a vote on a petition while the justices ask for a recommendation from the US solicitor general, the government's top lawyer before the court, that order -- which also takes four votes -- will appear on the public docket.

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That happened Monday in the copyright infringement case of Google v. Oracle America, and the order said simply, "The Solicitor General is invited to file a brief in this case expressing the views of the United States." No deadline was set.

Roberts sets the agenda and begins the discussion. The other justices then speak in order of seniority. For most cases, the justices' first impression is set by a memo produced by a pool of law clerks. Seven justices have their clerks join forces to screen the "petitions for certiorari," as appeals are formally called, to determine which ones should be accepted for oral argument and full review.

Clerks to Justices Samuel Alito and Neil Gorsuch do not participate in the so-called "cert pool" and separately cull the petitions to flag cases that the larger group might have rejected but would be of particular interest to them.

The justices have nearly complete discretion over which petitions they hear, and most are rejected outright. Before these weekly meetings, Roberts circulates a list of the handful of cases that he believes merit discussion.

These tend to be disputes involving a split in lower court opinions, causing inconsistencies across the country, or legal issues of clear national importance. The other justices may add items to the "discuss" list. Any petition that is not designated for discussion is automatically denied.

It is difficult to determine how many cases are discussed in the justices' cloistered confines. When questioned about various rules, the Supreme Court's Public Information Office referred to a book, "Supreme Court Practice," written by private appellate lawyers and published by Bloomberg BNA ( list price: $525 ), that estimates about 90% of the cases fail to make the discuss list and are rejected outright.

Occasionally, the justices grant a petition and later realize the legal issue is not sufficiently ready for resolution. That happened this week when the court abruptly dismissed a case brought by Emulex Corp., a subsidiary of chipmaker Broadcom, testing whether investors can sue for negligent misstatements or omissions in connection with a tender offer.

The case, which had drawn dueling high-priced lawyers and nine "friend of the court" briefs, including from the Department of Justice and US Chamber of Commerce, had been argued just a week earlier, on April 15.

Yet after all the attention put to it, the court ended it all with a one-sentence order, saying that the case had been "improvidently granted." There was no explanation or recorded vote. Dismissal, according to insiders, required agreement among at least five justices.

Strategy

Overall, as the justices decide which cases to take up, their votes may sometimes be more strategic than straightforward. Because it takes four votes to accept a case but five to resolve it, some justices will not risk hearing a controversial matter if they cannot count on a fifth justice on their side.

Individual justices might choose to avoid a case they may not win or that seems ill-timed based on other considerations. Rarely do such calculations burst into public view. But earlier in the current 2018-19 session, Justice Clarence Thomas suggested his colleagues had spurned an appeal because it involved Planned Parenthood and "a politically fraught issue."

The dispute was not related to abortion rights. Rather, it centered on Republican-led state efforts to deny Medicaid money for Planned Parenthood services to poor patients. Lower courts judges have issued conflicting rulings on whether patients may sue states under federal law for cutting off Medicaid providers.

When the Supreme Court majority rejected a petition by Louisiana officials, Thomas, joined by Alito and Gorsuch, dissented. The trio needed only one more vote to accept the dispute and schedule oral arguments. Perhaps at a different time they would have found the fourth in Kavanaugh or even Roberts. But in this highly polarized atmosphere, the chief justice appears to be trying to avoid ideological litmus tests at the court.

"Some tenuous connection to a politically fraught issue does not justify abdicating our judicial duty," Thomas wrote. "If anything, neutrally applying the law is all the more important when political issues are in the background. ... We are responsible for the confusion among the lower courts, and it is our job to fix it."

Dark of night

Tensions were even higher more recently in a series of orders related to prisoners seeking to elude scheduled executions.

As a preliminary matter, death penalty cases present distinct complications because the votes of four justices are enough to accept a petition related to a legal issue but five votes are needed to block an execution. In theory -- and sometimes in reality -- the court may muster the votes to review a prisoner's legal question but not to prevent his execution before a hearing.

The court's private rules say that if five justices vote to deny a stay of execution and four justices want to grant it and believe the petition has merit and should be heard, one of the justices who would let the execution proceed "may" change his or her vote for the requisite five.

As cases have demonstrated in recent years, however, such "courtesy" votes, as the practice has been called, have not been consistently cast

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The more recent string of contentious capital disputes began with a February 7 case from Alabama. A five-justice majority led by Roberts rejected a Muslim prisoner's request to have an imam with him in the death chamber. (Christian prisoners scheduled to die were allowed Christian ministers.)

The justices in the majority issued a simple two-sentence order letting the execution of Domineque Ray go forward without an imam at his side.

In a three-page statement on behalf of dissenters, Justice Elena Kagan wrote, "Here, Ray has put forward a powerful claim that his religious rights will be violated at the moment the state puts him to death. The Eleventh Circuit [appeals court] wanted to hear that claim in full. Instead, this court short-circuits that ordinary process -- and itself rejects the claim with little briefing and no argument -- just so the state can meet its preferred execution date."

A separate Alabama case provoked even more dissension, with an order coming just before 3 a.m. on April 12 and lifting a stay of execution on an Alabama murder convict. The case again pitted the court's five conservatives against the four liberals.

The conservative majority said that the prisoner, Christopher Lee Price, failed to meet a deadline for challenging the three-drug lethal injection that Price argued would cause him severe pain and suffering.

Breyer, joined by the three other justices on the left, wrote that the court was needlessly overriding lower court judges' views that the execution should be postponed and instead allowing "arbitrary" implementation of the death penalty. He also chastised his colleagues for declining to wait just a matter of hours for a regularly scheduled meeting in their conference room that Friday morning, April 12.

"To proceed in this way calls into question the basic principle of fairness that should underlie our criminal justice system," Breyer wrote. "To proceed in this matter in the middle of the night without giving all members of the court the opportunity for discussion tomorrow morning is, I believe, unfortunate."

Beyond his complaint about court process, Breyer asserted, "What is at stake in this case is the right of a condemned inmate not to be subjected to cruel and unusual punishment in violation of the Eighth Amendment." He was joined by Justices Ruth Bader Ginsburg, Sonia Sotomayor and Kagan.

In the majority were Roberts, Thomas, Alito, Gorsuch and Kavanaugh. The majority emphasized in their unsigned opinion the "last-minute" nature of Price's claim and the missed deadline.

They said nothing of Breyer's complaint regarding the absence of discussion. At least nothing that emerged in public view.