Logic and flow. Be easy on the reader. They really want to read your essay, but they don't want to have to work extra hard to figure out where you are going, or where you have come from. Build your story in a way that is easy to follow. Don't scatter related information around, keep it together.
Unnecessary words come into many peoples' writing at two levels.
First, you undoubtedly know a lot of material related to your paper, but it may well be better without information that is not central to your thesis. Second, many sentences become cluttered with extra words, if the word isn't necessary for the sentence, drop it. Avoid unless they are commonly used in papers you have read and you use them more than 3 times. Don't be shy, have one. There is frequently a rigid outline of how a paper should flow.