An Alberta man appealing a first-degree murder conviction has had his U.S. prison sentence reduced, after he pleaded guilty Monday to the second-degree murder of his wife in 2008.

Brad Cooper agreed to a plea deal in a Raleigh, N.C., courtroom Monday that allowed him to plead guilty to the lesser charge, according to local reports.

Cooper, 40, was previously sentenced to life in prison, with no chance of parole, in 2011 after being convicted of first-degree murder in the death of Nancy Cooper. But the conviction was overturned last year and another trial ordered.

Nancy Cooper disappeared from Cary, N.C., a suburb just outside of Raleigh, on July 12, 2008. At the time, her husband said the 34-year-old had gone for a jog and never returned.

Her body -- clad only in a sports bra -- was found two days later in a drainage ditch at the end of a cul-de-sac in an unfinished subdivision near the couple’s home.

On Monday, Brad Cooper responded “yes” when the judge asked if he killed his wife and dumped her body.

Cooper had his sentence reduced to at least 12 years in prison. He will receive credit for the five years in prison he has already served under the previous first-degree murder conviction.

During his 2011 trial, prosecutors alleged Brad killed Nancy because he was angry about her plans to divorce him and move back to Canada with their two daughters. The Coopers had moved to Cary, N.C., from Calgary in 2001 for Brad’s job, a year after they were married.

Witnesses previously testified the couple argued at a party the night before she disappeared, and that both had affairs outside their marriage.

The Appeals Court said Cooper was allowed a retrial because evidence in the case was largely circumstantial. The Appeals Court also said Cooper should have been allowed to call on experts to examine the evidence and testify on his behalf.

As part of his plea deal, Brad Cooper has agreed to let his daughters, now 8 and 10, be adopted by Nancy's sister.