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Biggest thing is sticking to your thesis statement. It is your guide. Don't stray from it. Avoid filler words or phrases that add nothing to the understanding of your topic. Every word should be working. Avoid long quotations. Instead paraphrase the idea into one concise sentence. Avoid technical jargon unless it is absolutely necessary. Saying it in simple non-technical terms is usually more concise and easier to understand. Use examples. Sometimes it is easier and more concise to explain a very complex idea by using an example. Instead of going to great lengths to explain something complex, use a few sentences to introduce and give a general definition of the concept and then use an example to illustrate the concept in concrete terms. Keep in mind the expectations of the customer or instructor. If the y want that lengthy explanation, that is what you give them, but even then tighten your writing so that the explanation is as concise as possible.
Great answer jag; you've given me the keys to concise writing.
To a Snail: If "compression is the first grace of style," you have it. - Marianne Moore, as cited by Joseph Williams * * * * If you want to look particularly at the structure of sentences in your search for concision, you might try Joseph Williams' _Style: Lessons in Clarity and Grace_ or the shorter version of the same book, _Style: The Basics of Clarity and Grace_. In these books, he devotes an entire chapter to revising writing at the sentence level so that it is tighter and cleaner. He talks about clearing away the "deadwood" and the deadwood for him falls into these categories: redundant pairs, redundant modifiers, redundant categories, meaningless modifiers, obvious implications, phrases for words, indirect negatives, excessive metadiscourse, hedges and intensifiers. He gives detailed examples throughout the chapter. It's a great book, in both versions. (There's another, related book on the same topic by Williams that you'll find if you do an Amazon search, but these are the two you'd want to focus on. They offer the same material but in updated form, and with exercises.)