She said, ‘What?’

When I’m writing the first draft, I don’t tend to stop to correct mistakes or adjust the prose; all that gets looked over again in the first round of edits. The second round is a little more detailed and tends to focus more on tightening things up and getting rid of the fluff, epecially in dialogue.
Every line spoken should move the story forward or tell you the reader something about the character, or preferably both. With that in mind, the first thing to go are those bits of repetition that crop up in real life but have no place in a book:

“I told you, Stuart. I intend to marry Harold!’
“What?” Stuart said, aghast.
“You heard me! Harold and I will be wed, this Saturday.”
“But . . . but . . . Harold is a chinchilla!”

Now it’s quite nomal for people to say “What?” during the course of a conversation. They will also say “Um” and “Ah” and “Well . . .” too, but you don’t include every single verbal tick in your novel, otherwise it would never finish. So in much the same way that you don’t include every nuance of speech, you need to look very carefully at every instance of “What?”

Remember that you’re not aiming to fill as much space as you can when writing a book, so every sentence, every piece of dialogue has to mean something.

“I told you, Stuart. I intend to marry Harold!’
“Then you’re quite quite mad, Diedre,” Stuart replied without looking up from his newspaper. “Harold is a chinchilla.”
“And he’s shown me more affection than you ever have!”

Unless they’re standing in a thunderstorm, assume your characters have perfect hearing. (Use some other device to convey the thunderstorm, not the dialogue.)

The other thing that’s worth bearing in mind when you come across “What?” is that it perhaps points to a whole section of dialogue that isn’t needed. When you’ve dumped the “What?” and the repeating dialogue below it, take a look at the line above. That could just be filling in space too.

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