Chris Foran / Milwaukee Journal Sentinel

“We Killed: The Rise of Women in American Comedy” by Yael Kohen (Sarah Crichton Books, $27)

In a way, it’s hard to understand why we’d need a book like “We Killed: The Rise of Women in American Comedy.” Women all but rule comedy in 2012, right? Kristen Wiig? Tina Fey? Amy Poehler? Ellen DeGeneres?

Ask Adam Carolla. The former co-host of “The Man Show” — whose “Adam Carolla Show” is considered, at more than 60 million downloads, the world’s most popular podcast — told the New York Post this summer to forget “30 Rock,” “Bridesmaids” and “Parks and Recreation”: Women just aren’t funny.

“The reason why you know more funny dudes than funny chicks is that dudes are funnier than chicks,” he told the Post.

Carolla’s not exactly an A-list guy, but his comments struck a nerve that’s been hit so often any contact elicits a cry of pain.

As “We Killed” author Yael Kohen points out, Carolla is not alone. Comedy legends from Johnny Carson to John Belushi to Jerry Lewis all made the pronouncement.

Kohen’s new book, “a very oral history” of women in comedy, sets out to show they’re wrong.

While it could use more, well, more funny itself, “We Killed” does clearly depict how the entertainment-industrial complex has made it hard for women to show they are as funny as men.

Why don’t women get more respect in comedy? As with many things in America, it’s all about opportunity.

From the first, “We Killed” shows, women had to fight to get male club owners, TV producers and agents to give them a shot on stage.

Joan Rivers, probably the most successful female comic of the 1960s, recalls how she auditioned for “The Tonight Show” eight times before getting a shot — and only then because Bill Cosby recommended her.

The Rivers anecdote is one of the few he-said-she-said moments in “We Killed”; if anything, the stories recounted by women comics (and the men who appreciate them) have a sameness after a while — unfortunately, because women trying to make their way in comedy have faced the same sexism decade after decade.

Opportunities only started increasing in the late 1960s and early 1970s, when women who got a chance to go mainstream in comedy gave a hand to other women. Lily Tomlin and Mary Tyler Moore helped foster not only the careers of female comedy writers on their television shows but boosted the roles of actresses they worked with.

As a history of women in comedy, “We Killed” is erratic, in part because of the voices that aren’t in it. Elayne Boosler, who several comics point to as the most important — and for a while, the only well-known — female stand-up comic of the 1970s — isn’t heard from; likewise Marsha Warfield, whose spot-on stand-up led her to a long stint on the sitcom “Night Court.”

But “We Killed” does fill in some gaps and yields some surprising perspectives on comedy of the past half-century. (Who knew Janeane Garofalo was so influential on stand-up?)

And it shows that, yes, women are funny — even if they have to keep proving it over and over again.