Barbra Streisand didn’t want to write about ex-partners in the book “My Name is Barbra – The Hollywood Reporter”.

With her new memoirs My name is BarbaraBarbra Streisand says she hopes readers finally learn “the truth” about her.

“One of the reasons I wrote the book is to talk about the myths about me,” Streisand tells CBS News’ Gayle King in an interview that aired on CBS Sunday Morning.

In addition to reflecting on her career as a singer, actress and director, Streisand writes about her “past loves and regrets,” as King teased.

But if Streisand, who has been married to James Brolin for 25 years, had her way, there would have been less coverage of her past relationships – including with Don Johnson, Ryan O’Neal, Andre Agassi and former Canadian Prime Minister Pierre Trudeau – in the book.

“Listen, I didn’t want to write about any of them,” Streisand says. “[But] My editor said, ‘You have to leave some blood on the page!'”

After King complimented it Just as we were star is on her “very nice dating list,” she asks Streisand if she had “a good time.”

“With the men in my life, yes,” she replies.

Elsewhere during her conversation with King, Streisand, joined at one point by Brolin and recalling the apparent insult her courtship caused, reflects on her childhood, including how “angry” she was over her father’s death was when she was just a year old and her mother’s lack of affection.

Despite her iconic career, Streisand also insists: “I don’t consider myself a famous person, I just don’t. I’m the same Barbara Joan Streisand I was in high school.”

The multi-hyphenate also tells King about the work that she finds most fulfilling: “I love directing because it’s a complete vision. … It demands every aspect of yourself: decorating, visualizing, helping actors deliver the performance I envisioned for them.”

Watch the full interview below, in which King also tours Streisand’s private shopping center in the basement of her Malibu home.