One way to make sure your writing is clear (beyond writing "good sentences") is to take a look at the content of your paragraphs. The technique I'm going to detail in this post is perfect for a first draft, but can be used for final drafts too. I like to use this method when I need to cut some words to make a paper shorter, or before and after a large reorganization of a paper.
The great thing is that this technique works for almost any kind of writing, creative or academic. When I worked with slam poetry teams, we used a version of this exercise, but it's also great for essays, or even presentations: each slide of your presentation is a "paragraph" in these examples. All that matters is that you have a draft ready to go of whatever type of writing you’re doing.
How to streamline a draft (for any kind of writing!)
Step 1: Skim + summarize
In this first step, skim through your paper as-is and try to identify the main theme of each paragraph. Take a pencil (or add a comment to the file you’re working in) and write down one keyword next to each paragraph that summarizes its content. Think of this theme or topic as the purpose of the paragraph. If you are having trouble thinking of just one word or phrase, you might have too much information for just one paragraph! This can help you figure out where to break larger paragraphs into smaller ones.
If you’re looking to make sure your ideas flow in a reasonable way, read through your list of keywords as if they were the paper: do the keywords make sense next to each other? Do you go back and forth between keywords a lot? If you’re jumping around and repeating themes, you might want to reorganize some of your paragraphs.
Step 2: Let the summary lead
After you've identified the theme or goal of each paragraph, it’s time to investigate each section on its own. Read through your prose carefully, one paragraph at a time. First, look at the keyword you chose to represent the paragraph, and then compare each sentence to that keyword. Is there a sentence that doesn't directly contribute to that central idea? If so, you might be able to cut it out, or move it somewhere else in your paper.
Step 3: Solidifying the narrative structure
Depending on what type of paper you're writing, and your word limit allowance, you might want to do one last check: read the first and last sentence of every paragraph and see if you can understand the main ideas of the paper without the details in each paragraph. In some types of writing, like in scientific abstracts, there's not enough space for nicely flowing transition sentences, and you may have explicitly labeled headings instead (like for sections and subsections). Either way, you want to make sure something is doing the work of laying out the path for the reader.
If you’re struggling organizing your thoughts, try adding explicit section headings to paragraphs or groups of paragraphs. These can work as an outline (or come directly from a detailed outline, even) and you can replace the explicit structure with narrative prose later on.