"My dad used to say, 'Get a grip. You need a career, get a job. You can't sit in a garret writing books all day,'" said Linda Fairstein, who for 30 years prosecuted sex crime cases in New York City. Today, the New York Times best-selling author is considered one of the finest crime fiction writers.

"This great career in the law gave me books," she said.

Best-selling crime writer Linda Fairstein. CBS News

"Deadfall" is Fairstein's 19th novel featuring fictional prosecutor Alexandra Cooper. "I'm actually 24 years older than when I first created her," Fairstein said Monday on "CBS This Morning." "She's aged three years, which is pretty nice! Physically she was 35, she's now only 38. But she's learned from the experiences.

"It's not easy to work with victims of violent crime, especially in sexual assault [or] domestic violence areas. So you see that change in her throughout. Several books ago she was kidnapped, obviously got out of it fine, but she's had some PTSD that she's dealt with, and this event sort of brings her, in 'Deadfall,' back to it."

During her years as a New York City prosecutor Fairstein was referred to in the tabloid press as "Hell on heels." Was it a compliment?

"At the time I didn't much think so," Fairstein laughed. "The Daily News did it; it was not what my colleagues did. But once the headlines ran, there was a lot of teasing, and that was fun."

Dutton

Her latest novel opens shortly after her last book, "Killer Look," ended with the murder of a major character at the Met Ball gala. "Easiest book I ever started," Fairstein said. "Because last year's book ends with a murder. This one, I knew an hour later that Alex would be in the morgue with the victim, whom she knew. He actually fell into her arms when he was killed, so she's got bloodstains. I turn the tables on her, and without thinking [she] becomes a suspect in the new book right away."

Fairstein said she didn't originally view writing about the "dark world" she's investigated — in real life and in print — as being cathartic, "but it is. People thought, 'Why do you do this work? It can't be rewarding. It's just dark.' And for me it was richly rewarding, because we were getting for the first time justice in court for victims of this kind of intimate violence. So to write about it, I think, helped me work through a lot of the issues, and then give it to the reader."

When asked how she has improved as a writer, Fairstein credited other mystery writers, such as Harlan Coben, Lee Child, Mary Higgins Clark and Lisa Scottoline. She also said David Baldacci probably changed her writing style without even knowing it.

"I had written three books," she recalled. "My late husband and I had lunch with him, and in prep for the lunch my husband raced through a bunch of his books, and he said, 'David, you end every chapter with a tease. You make me want to page-turn at the end of every chapter. I can't go to sleep!' Kind of every writer's dream. I thought maybe it's something I ought to. So I credit David Baldacci's style."