Barbra Streisand Was Told She Had to Write About Exes in New Memoir

Barbra Streisand has a had a long, healthy love life -- and while she says she didn't really wanna talk about it in her new book ... the powers that be told her, spill it sister!

The iconic pop star -- whose memoir, 'My Name is Barbra,' hits shelves everywhere Tuesday -- sat down with CBS Sunday Morning this weekend for a chat with Gayle King ... who chopped it up with her about her storied career, but also -- about the men in her life.

Watch ... Gayle points out that BS has quite the resume under her belt -- rattling off some names like Don Johnson, Ryan O'Neal, Andre Agassi and even ex-PM Pierre Trudeau ... just to name a few.

You can tell it embarrassed Barb, but she tells GK straight up ... if it was up to her, none of those fellas would've been name-dropped in her memoir, but she was pushed into it.

Unfortunately for her (and luckily for us) ... she says her editor told her she had to spill the dirty deets and "leave blood on the page" in order to move copies -- and it sounds like that's exactly what she did. BTW, she's currently married to Josh Brolin's dad, James.