HONOLULU — An “evil” stepmother derived pleasure from severely beating her husband’s 5-year-old daughter while they lived in Army housing in Hawaii, a federal judge said Tuesday as he upheld a plea deal the woman made with prosecutors to receive a 20-year sentence for the murder of the child.

Though the agreement with Delilah Williams seemed distasteful and “difficult to swallow,” U.S. District Judge J. Michael Seabright said it was necessary in prosecuting a murder case against her husband, Naeem Williams, who prosecutors said delivered the punch that killed his daughter Talia on July 16, 2005.

“There are only three people in the entire world that knew the truth about what was happening in the Williams household,” Seabright said. “Obviously, Talia is not here to tell us her story about what happened. ... So the government made a deal with the only person who could provide the whole story and that was Delilah Williams.”

The judge said he had wondered if a prosecutor was exaggerating in his opening statement when he called her a “wicked stepmother.” But her testimony proved the prosecutor’s characterization was accurate, Seabright said.