PHOENIX — A federal appeals court refused Friday to overturn the conviction of a man in connection with a 1992 robbery and triple murder in a Tucson market, saying any lies told by a detective were not material.

In a divided ruling, the three-judge panel of the 9th U.S. Circuit Court of Appeals did not dispute that Tucson police Detective Joseph Godoy had lied about how he came to see Martin Soto-Fong and two others as suspects in the incident at El Grande Market. And Ken Peasley, who prosecuted the case, was subsequently disbarred after the Arizona Supreme Court concluded he knowingly solicited false testimony from Godoy at the separate trials of Soto-Fong’s co-defendants.

But Judge Robert Timlin, writing for the majority, said a review of the testimony in this case fails to convince him that Godoy’s testimony was false or misleading. So he said the three consecutive life sentences should stand.

That conclusion drew criticism from Judge Mary Schroeder, who said the trial was “marked by perjury and incompetence.” She said Soto-Fong should get a new trial.

Soto-Fong and two others were charged with robbing the former south-side market, killing Fred Gee; Huang Zee Wan, who was Gee’s uncle; and Raymond F. Arriola.

In an earlier ruling, the Arizona Supreme Court found that Peasley allowed Godoy to falsely testify that Soto -Fong, along with Christopher McCrimmon and Andre Lamont Minnitt, weren’t suspects before getting a tip from an informant. But there had actually been an earlier investigation of the trio.

Minnitt’s conviction was eventually overturned; McCrimmon was later acquitted. And the state’s high court, in that latter case, said Peasley “engaged in extreme misconduct” that was “grossly improper and highly prejudicial” to Minnitt and the entire criminal-justice system.

But Soto-Fong had his own appeal to the Supreme Court rejected. So he sought relief from the federal appeals court.

Timlin said there may be “inconsistencies” between Godoy’s testimony at Soto-Fong’s trial and other evidence of what information the detective had and when he got it. But the judge said that even if Godoy’s testimony “was not fully accurate,” the jurors did finally get the complete story and any false impressions were corrected.

Schroeder, however, said Godoy’s testimony was false and that it bolstered the statements of the informant, whom she described as someone who had only recently been released from prison “and, absent cooperation, would have soon been back in prison on a drug charge.”

Perjury questions aside, the judge said Soto-Fong should get a new trial because of incompetence by his trial lawyer in calling the informant as a witness in the first place, a witness who could not testify on behalf of the prosecution.

She said it is “quite possible” that Soto-Fong would have been convicted without that testimony.

“But with that testimony, there was no way that the jury could have failed to convict Fong,” Schroeder wrote. “His own lawyer put the nail in his coffin.”

Soto-Fong, 17 at the time of the killings, had originally been sentenced to death. But that was before the U.S. Supreme Court voided the death penalty for juveniles. A judge then sentenced him to three consecutive life terms, each with a minimum of 25 years behind bars.