The state has sweetened its plea offer once again to a man accused of fatally strangling José Cartagena in Groton four years ago, and the defendant, Dirren Conyers, has once again rejected the deal.

Conyers, 35, of Groton was charged with first-degree manslaughter and first-degree unlawful restraint after a melee in front of a Miami Court, Groton, home on April 13, 2008, that resulted in Cartagena’s death.

He has rejected a third offer from New London prosecutor Paul J. Narducci to plead guilty to a lesser charge in exchange for a reduced prison sentence. Had he accepted, he would have pleaded guilty to second-degree manslaughter and would have been sentenced to 10 years in prison, suspended after six years served, and five years probation.

His case remains on the trial list, and during his appearance in Superior Court Monday morning, Judge Patrick J. Clifford told him the case is a priority since it’s so old.

Conyers, who is free on a $250,000 bond, rejected an initial offer to plead guilty in exchange for a prison sentence of 20 years in prison, suspended after 15 years served, and five years’ probation.

In 2011, he turned town a second offer involving a sentence of up to 10 years in prison.

According to court documents, Cartagena, 36, died after tangling with a group of people who had gathered outside a house on Miami Court after closing time at Sully’s Cafe, a local bar. At one point, seven or eight people were kicking and punching him as he lay on the ground, according to a witness.

Conyers is accused of placing Cartagena in a choke hold until he stopped breathing. Police also charged a second man, James D. Smith, with unlawful restraint, third-degree assault and second-degree breach of peace. Smith’s case is pending.

— Karen Florin