A Little Falls, Minn., man who is serving two life sentences for killing two teenagers who were burglarizing his home in 2012 has filed a “notice of appeal” with the Eighth U.S. Circuit Court of Appeals, alleging that a brief closure of the courtroom denied him his constitutional right to a public trial.

The notice Wednesday is the latest in a series of legal filings by Byron Smith to have his convictions overturned.

Byron Smith had argued in a petition to the Minnesota Supreme Court that the trial court judge denied him his right to a public trial because he briefly closed the proceedings to spectators and the media before the opening statements to discuss some evidence. After the court rejected that argument, Smith’s attorney, Steven Meshbesher, filed a petition in federal court in Minneapolis seeking to overturn it.

Chief U.S. District Judge John R. Tunheim rejected that petition Aug. 3, ruling that the state Supreme Court’s ruling was “neither contrary to, nor an unreasonable application of, clearly established federal law.…” But he also found fault with the court’s ruling and issued a “certificate of appealability” so that it might be reviewed.

Smith fatally shot Nicholas Brady, 17, and Haile Kifer, 18, on Thanksgiving Day 2012 as they broke into his home. Smith claimed self-defense and sought to introduce evidence that Brady had been involved in earlier burglaries of his home. To do so, he wanted to call Brady’s mother and two of his friends who also were allegedly involved to testify.

Morrison County Judge Douglas Anderson issued an order saying that Smith could introduce evidence of earlier burglaries of Smith’s home through the testimony of law enforcement agents, but he barred Smith from introducing evidence of Brady’s involvement because Smith was unaware of that at the time of the shootings.

The morning the trial was set to open in April 2014, Anderson closed the courtroom briefly to explain the scope of his earlier ruling, including that there should be no public mention of the names of Brady’s friends who allegedly had been involved with him in earlier burglaries. He said he had excluded the public and the media because he didn’t want those names made public.

The Minnesota Supreme Court ruled that the closure was an administrative proceeding to which the public-trial right does not apply.

Tunheim’s 30-page opinion expresses some misgivings about the purpose of the closure, and he “expresses significant concern” with what he calls the trend in Minnesota “toward more restrictions and closures — irrespective of whether they are classified as true, total, partial or otherwise. Indeed, members of the Minnesota Supreme Court themselves have criticized this ‘creeping courtroom closure,’ ” he wrote.

Tunheim concluded that in deference to the Anti­terrorism and Effective Death Penalty Act of 1996, “some constitutional violations will go unremedied by the federal courts, but not unnoticed. This is likely one such case. Despite the relatively short closed interruption in the trial, the Minnesota trial court appears to have violated Smith’s Sixth Amendment right to a public trial,” though it may not have run contrary to clearly established federal law.

He said the Minnesota Supreme Court may have had good intentions, but its decision “and the precedent on which it relies demonstrate precisely the risk of a slow but steady erosion of constitutional rights by the well-intentioned that must be vigilantly guarded against.” He warned that if Minnesota courts don’t curb their practice of closing courtrooms during criminal trials, “Minnesota might soon find itself in Georgia’s shoes: on the losing end of a summary reversal by the Supreme Court of the United States.”

Noting that some other court could resolve the matter differently and that the issues deserve further review, Tunheim granted a “certificate of appealability” so that his opinion could be reviewed by the Eighth Circuit.