In an interview on the tompeters.com site, Garrison Keillor said this about what he’s learned about writing and rewriting:
“When you're young, you're so fond of what you have created, because it takes a lot of effort to extrude this onto the page or onto the screen. You're very fond of it, even if it's wounded and you're barely alive, you still have affection for it.
But as you get older, you learn how to throw it out without much thought, without much pity. You look at a piece that you've written, and you take those first three paragraphs, and you dump them. You just rip them out. Usually, that's the part that needs to be thrown out, the big windup, the big introduction. The first page almost always can go. You learn to do that without regret. I edit myself much more quickly and mercilessly now than I ever could have 20, 30 years ago.”
Here’s what he said about openings (he’s talking about a live presentation but I think it applies to the first paragraph or two of anything you write as well):
“I think anybody in the business knows that the first sentence out of your mouth, the first minute you have in front of an audience is crucial, absolutely crucial. The audience is going to give you the benefit of the doubt for at least a minute or two. So don't waste that.”
(Tips about capturing your readers' attention and other ways to make your writing compelling are in my book, "Your Writing Coach," published by Nicholas Brealey and available from Amazon and other online and offline retailers. You may also want to check out my newest book, "Creativity Now!" which features 25 ways to get into a more creative state and 25 ways to generate ideas.)