NASHVILLE, Tenn. — A federal judge on Wednesday overturned the convictions of three men on sex-trafficking charges in an alleged widespread conspiracy that prosecutors said spanned three states. The other six defendants tried in the case had been acquitted previously.

U.S. District Judge William Haynes said his decision to overrule the jury was based on the government’s failure to prove the men were part of a single, overarching conspiracy. The men had been convicted on a charge of conspiracy to commit sex trafficking of children.

Haynes also concluded that even if the acquittal were to be overturned on appeal, the defendants still are entitled to a new trial because the government failed to turn over thousands of pages of documents to them before the start of trial in April.

Some of those documents showed contradictions in the testimony of the government’s principal witness, a young woman known as Jane Doe Two.

The victim testified in the trial that lasted more than two weeks that she was used as a prostitute in the Minneapolis area starting at age 12. But the defendants have supplied new evidence that suggests Jane Doe Two may have lied about her age.

Assistant U.S. Attorney Van Vincent could not be reached for comment by telephone or email after business hours on Wednesday.

Defense attorney David Komisar said he believes Jane Doe Two was 18 or 19 years old when she went out with his client Yassin Abdirahman Yusuf, who was 19 at the time.

“So they were about the same age when they go out on this wild weekend, and all of a sudden he’s picked up on conspiracy sex-trafficking charges,” Komisar said. “And it wasn’t true.”

Komisar said that Yusuf and the other two defendants — Idris Ibrahim Fahra and Andrew Kayachith — will have to face a new trial only if the government appeals the acquittal and wins. Otherwise, the case is over.

Yusuf is “very, very happy at the prospect of getting out of jail,” Komisar said. “He’s been in jail two years.”

Originally, 30 people were indicted in the case that spanned Ohio, Minnesota and Tennessee. Government prosecutors claim they were members of a Somali gang that ran a prostitution ring involving underage girls. Only nine of the original 30 stood trial in April and six were acquitted by the jury.

In June, Haynes dismissed charges against another three of the original 30 defendants because they were juveniles at the time the alleged crimes occurred.

The remaining defendants still could face trial at a later date.