He also pleaded guilty to choking to death Lisa Pate, covering her head with a plastic bag, in 1999 after she refused to stay in a Lafayette motel with him, instead wanting to return to her children in Youngsville.
By pleading, he avoided execution and will spend the rest of his life in prison.
In his signed statements, Lavergne admitted to grabbing Shunick off St. Landry street in Lafayette as she pedaled her bike home about 2 a.m.
He had been driving around the city, calling escort services in an unsuccessful attempt to get a date.
He bumped Shunick’s bike from behind and then persuaded her to get into his vehicle, either with or without her consent.
Inside the white pickup truck, Shunick, the statement said, grabbed her cell phone and Lavergne threatened her with a knife.
She sprayed him with a can of Mace, took the knife and stabbed her several times, inflicting serious wounds.
Lavergne grabbed the knife back and said he stabbed her four times and she slumped over. Checking for her pulse, he found none.
Thinking the 22-year-old coed dead, he drove to a cane field in North Acadia Parish to dispose of her body, thinking she was dead.
As he stopped in the field, Shunick jumped up, again armed with the knife.
Lavergne told the court through his statement that he then shot her in the head, killing her instantly.
He drove to the Evangeline Parish cemetery site where her body was eventually found to bury her but was too weak from the wounds he had suffered, so covered the body with branches and woods.
After disposing of various evidence, he contacted an out-of-town acquaintance and arranged a visit to establish an alibi.
Enroute, he dumped Shunick’s bike at Whiskey Bay. During the same trip he received treatment in Metairie for the injuries his victim inflicted.
He subsequently returned to Evangeline Parish and buried Shunick in the shallow grave he led police to last week after bargaining for his life.
After that, he arranged to take his truck to Texas, burn it and get another, hoping to obliterate a vehicle trail to him.
Documents introduced at Friday’s hearing indicate Lavergne told inmates of killing Pate.
He served 10 years in state prison for a sexual assault in Evangeline Parish, an assault that occurred several months after Pate’s killing.
Lavergne was a suspect in the investigation at the time, but police were unable to close the evidentiary noose.
This time they did.
Sources said Lavergne’s decision to bargain rather than take his chances at trial and face possible execution was in part due to evidence which never became part of the official record