Oh! I've got it! I'll put him in porn!"
Action Comics #593
This issue's been covered and mocked and stood in awe of a million times on the internet, so I'll keep this short. A villain from Apokolips kidnaps Barda, superhero and wife of fellow superhero Mr Miracle. He hypnotizes her and starts filming her doing porn. Yeah. Same villain grabs Superman and does the same because he thinks, "I'm making a fortune with one superhero, but what if I had two!"
Seriously, what the hell were you thinking Byrne? And who the hell approved this? On what the hell planet is this an acceptable story for children?
Want to see Byrne's lame ass defense of the story?
In the ACTION COMICS two-part storyline involving Big Barda, Miracle Man and a character called Sleez, it appears that Sleez was trying to film a pornographic film involving Superman and Big Barda. Is that right? Did Superman and Barda actually make the porno?
JB: If you want it to be a porno flick, it was a porno flick. If you don't, it wasn't! (8/31/2005)
Superman snapped out of the hypnosis before actually sleeping with Barda due to his strong moral fiber. Barda didn't though, because apparently deep down she wants to cheat on her husband on camera.
Jack Kirby hated this story, by the way. (And by all accounts generally thought Byrne was a douchebag all around.) He felt it was an inappropriate use of his characters and Superman. Fun fact: Kirby modeled aspects of Barda's personality on his wife. Barda. The character Byrne put in porn. And Byrne claims to not understand why Kirby didn't like the story.
Edit to add: You really should read the comments on this one, Russell knocks it out of the park.