There have been a few cases where I've asked a question on StackOverflow, and received a number of good responses which then made me realize that there was a much better/clearer/more concise way to to ask my original question. I know I can edit my original question, but I'm always hesitant to rewrite the original question for fear that parts or all of the current responses will no longer make sense.
What is the preferred course of action when this happens? Should I just post an entirely new question? Or edit the existing question, which may very likely lead to the current responses no longer making sense?