Write that document. Then, let it sit. Preferably, let it sit for 24 hours.
Then, re-read it. It's almost guaranteed you'll end up tweaking the document. You might add a fact that you accidentally omitted in the heat of the moment the day before. Or, more likely, you'll alter the tone so it will achieve a better response from the document's recipient. You may even decide not to send the document at all, and instead will discuss the matter in person or over the phone with the intended recipient.
Usually, time and circumstances permit you to let your document sit for a day. And when your document sits for a day, you'll end up ultimately crafting a better message.