A man who killed his 3-year-old son by throwing the boy off a bridge in Baltimore will face a maximum sentence of 50 years in prison under a revised plea bargain, authorities said.

Stephen T. Nelson, 40, pleaded guilty Tuesday to second-degree murder and child abuse resulting in death.

On Monday, a judge rejected a plea deal that called for Nelson to serve a maximum of 30 years, calling it "too light under the circumstances." The case was sent to a different judge for trial, and attorneys negotiated a deal with a 50-year sentencing cap.

Nelson acknowledged that he threw his son, Turner Nelson, off the Francis Scott Key Bridge into the Patapsco River in February 2008. Prosecutors said the man had been arguing with the boy's mother over a transfer of custody, and after killing his son, he tried to commit suicide by drinking cleaning chemicals. The boy's body was found 5 months later.

Natisha Johnson, the boy's mother, wept in court as Assistant State's Attorney Julie Drake read the facts of the case. After throwing the boy from the bridge, Nelson called Johnson and told her, "I killed our son and it's all your fault. You're going to have to live with this in your heart."

Johnson said after the hearing that she was satisfied with the plea arrangement.

"It gives me a whole lot of closure," she said.

Johnson was eager to see the case resolved, Drake said.

Robert Linthicum, one of Nelson's public defenders, said his client also did not want to go through the ordeal of a trial.

"It's a fair resolution to a difficult case," Linthicum said.

Attorneys for both sides downplayed the significance of longer maximum sentence.

Drake said her goal in pursuing the plea deal was to ensure that Nelson went to prison and not to a "cushy mental hospital." As part of the deal, Nelson's attorneys withdrew a previous plea of not criminally responsible — the equivalent of an insanity defense.

"The primary concern was making sure that the defendant was held accountable for what he did," Drake said.

Drake said she believed Nelson was criminally responsible for his actions but couldn't be certain that a jury would agree.

Attorneys revealed Tuesday that Nelson had suffered a stroke around the time that he killed his son. Linthicum said that was one of many mitigating factors the defense planned to present at sentencing, scheduled for Jan. 28.