When it comes to culture, I’m probably more permissive than most parents. I read H. P. Lovecraft to my 7-year-old, Penny, and also showed her “Jaws” and “Alien,” but it wasn’t until I took her to a comedy club that I felt truly irresponsible.

Parental guilt started sinking in after I persuaded a skeptical ticket taker at Carolines on Broadway to let a child see a headliner one Friday this month. As we waited for the opening acts to finish before we entered, I considered the many kinds of jokes I would not want Penny to hear and the years of therapy required to repair the damage. Noticing my mounting anxiety, she asked, “Daddy, are you about to make a mistake?” I answered honestly: “Maybe.”

At a time when comic-book heroes dominate Hollywood, cartoon characters regularly invade Broadway and kids’ karaoke entertains crowds of thousands, live stand-up remains stubbornly family-unfriendly. Few clubs are for all ages, and there is no stand-up version of the singer Dan Zanes, a star for young audiences.

Why do stand-up comics cede this market to clowns and magicians? Would kids even like performers holding microphones telling jokes onstage? Seeking some answers, I took my daughter to shows looking for comedians she would find funny and I wouldn’t find inappropriate.