For 35 years, she was known only as Blue Earth Jane Doe.

On Tuesday, authorities finally gave her a name.

New DNA testing proved that the badly decomposed body found in a southern Minnesota drainage ditch on Memorial Day 1980 had been Michelle Y. Busha, an 18-year-old Texan who was hitchhiking across the country, authorities announced at a news conference Tuesday.

Busha was found about a mile downstream from where she was handcuffed, raped and strangled by a state trooper after she rebuffed his sexual advances, according to officials of the state Bureau of Criminal Apprehension.

The trooper had stripped his ­victim of everything he could to deny investigators any chance to identify her at the time.

The woman's body was exhumed in August from a Blue Earth cemetery, and authorities made a DNA match that revealed Busha's identity.

"We have some answers after 35 years of waiting," said Catherine Knutson, BCA Forensic Science Services director, after putting a name to the victim who spent years in a grave site marked "Unknown Caucasian female."

Robert LeRoy Nelson was charged eight years after the slaying, in 1988. He eventually pleaded guilty to first-degree manslaughter in the death of Busha.

Nelson, 43 at the time he was charged, was sentenced to life in prison. He is in a prison north of Houston, Texas, where he is also serving a separate sexual assault sentence.

"This was not a case of who done it, but who was she," Faribault County Sheriff Michael Gormley said.

Gormley said Busha's relatives are "glad to know where she is at now. They were surprised that she was up here."

In his confession, Nelson said he saw a woman exit a vehicle along the interstate near the Bricelyn overpass. He said he approached and offered her a ride, which she accepted. Nelson detailed how he sexually assaulted, handcuffed and killed Busha before dumping her in the drainage ditch. Her naked body washed up after heavy rains some time later and was discovered by a farmer, floating among corn stubble and grass.

Busha's body was exhumed as part of the BCA's unidentified human remains program. The exhumation led to a positive hit from the national DNA database, connecting Busha to her family. Two relatives had submitted samples to the database in 2007. Authorities also had blood from the crime scene.

"Advances in forensic science led us to information we couldn't obtain in 1980," Knutson said. "Key to our success was Michelle's family's decision to provide DNA samples. Without that information in the system, we would not know who she is today."

After the killing, Nelson moved with his wife and three children to Vergas in northwestern Minnesota, where he worked out of the State Patrol office in Detroit Lakes. He later joined the Into the Light Ministries, a small Christian end-times ministry founded by a former pop musician. Nelson resigned from the patrol in 1985, sold the family belongings at auction and moved to Texas with the group.

Nelson confessed to being responsible for a Minnesota slaying while being ­questioned in Texas in June 1988 for sexually assaulting a child. He also was charged and later convicted in Faribault County in another case involving sexual assault.

Jerry Kabe, a retired Faribault County sheriff's deputy and the lead investigator in the 1980 killing, said Nelson had thrown away Busha's clothes, jewelry and purse, robbing investigators of any clues to identify her.

At the time, authorities hoped to identify her through her dental records or fingerprints, but were unsuccessful.

"Back in the '80s, missing persons cases were not treated the same way they are today, mostly because options were so limited," Knutson said.

DNA technology has also come a long way, she said.

In the 1980s, Knutson said, authorities "would need a stain about the size of a quarter … in order to get enough information about identity."

Recent scientific advancements have shrunk the needed sample size down to the tip of a ballpoint pen, she said.

The story caught the eye of Deborah Anderson, a Blue Earth resident who says she became intrigued after an old police friend mentioned the case.

After visiting Busha's grave site, Anderson devoted herself to finding out her true identity, passing out fliers and registering her case on national missing persons clearinghouses.

Anderson says that she has spoken with Busha's sister since the news was announced and said they were having a difficult time coming to grips with the "bittersweet ending."

The grisly murder left an imprint on law enforcement, too.

Kabe, now 75, said the slaying kept him up many nights.

"A murder like that doesn't leave your mind," he said. "You live with it."

Authorities said the next step will be to return Busha's remains to her native Texas.