When getting my essays down to the word limit, I found that I had two habits, which I learned to break.
1) Even in conversation, I tend to use two or more words that mean the same thing, when just one would do. For example, I might say something like "achieve the project's results or goals." Well, "results" and "goals" mean the same thing here. So I studied every sentence I had that contained an "or" to see if I could eliminate words.
2) The other thing I found was that you need to strike the right balance between providing enough detail so that the reader stays engaged with your story and follows the sequence of event vs. providing too much where you get bogged down and the reader is starting to lose the plot and probably will start to skim. I think this is especially true of work stories. B school admissions officers don't work in your industry and so they won't understand every minute detail that might be important to you because you actually do the job. And reading thousands of leadership project stories can get really repetitive.
So you do need to provide some detail and explain anything that needs explaining, but I found that I was trying so hard to *really* explain why the project was a success for my company that I lost sight of the larger message about leadership, teamwork, my confidence, etc.