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Brainstorm your ideas. Know your purpose. Know your reader. Research the topic.
Before you start your letter, brainstorm. Make sure it states what you want, why you want it, reasons why it should be granted, and any arguments against you. Is this really the topic you want? Getting your ideas down can help you clearly draft your letter and fully understand your position on the topic.  Start by using this: I want to persuade my audience to my purpose. Exchange my audience with who you want to persuade and my purpose with what it is you want to persuade them to do. After you have established that, ask yourself: Why? List the reasons why you want your audience to do what you want them to do. After you brainstorm reasons, sort them by importance. Place all the important details into a column, then place all the less important details in another column. This step helps  you narrow your reasoning so you emphasize the relevant, salient points. Make sure you know exactly what you want or need. What are you trying to accomplish? What do you want to happen? When you are figuring out your purpose, think about any solutions that you can offer. Analyzing and understanding your audience will help you decide how you should frame your letter. If possible, determine if your reader agrees with you, disagrees with you, or is neutral. This will help you decide how much weight should be placed on each side of your argument.  Try to find a real person to address your letter to. Who are they, and what power do they really have to help you? How are they going to change your mind? Will they just pass along your complaint? How should you address them? Are they in a senior or functionary position? Talk to them according to their position. Try to discover what beliefs and biases the reader has about your topic. What disagreements might arise between you and your reader? How can you present a counterargument respectfully? Figure out what concerns your reader might have with the topic. Do they have limited funds to distribute? Are they directly affected by the topic? How much time do they have to consider your document?  Think about the kind of evidence your reader will need in your argument to be persuaded. Effective persuasive letters contain factual evidence and information that supports the position. Make sure to consider multiple points-of-view. Don't just research your side; mention the contrary opinion and facts surrounded it.  Use facts, logic, statistics, and anecdotal evidence to support your claim.  Don't come out and say the other side is wrong; instead, be respectful as you explain why your position is stronger and deserves notice.