According to David McCullough and HBO, Jefferson's first draft of the Declaration of Independence was 'We hold these truths to be sacred'. Then, in the writers room, Ben Franklin and John Adams rewrote it out loud into 'We hold these truths to be self-evident', improving the cadence and trumping even God.

I also read recently that the original American Santa Claus' line was 'HO HA HO'. It was subsequently rewritten by some anonymous 19th century copywriter to the familiar, and let's face it vastly superior, 'HO HO HO' - a rewrite that clearly happened when someone heard the line out loud and (probably subconsciously) realized that 'HA' put the stress in the middle instead of at the end where the line has landed ever since.

For your own rewrite process, the key is being able to see your material with fresh eyes. And hear it with fresh ears.