Concision does not necessarily equal short. It means your text is free from superfluous details and it has a high idea/word ratio. The primary advantage of writing a concise text is that your reader will get more ideas by time spent reading.
Making your text concise is better done when editing. You write the whole text first as you will, then, on rewriting, you start cutting things out. Here are some tips on what to cut to make your text more concise.
Delete unessential words. If you can remove a word and the meaning of your sentence remains untouched, remove it. In literary writing, you include words that mark your style for an emotional effect. This might also be applied to job-related communication. Usually for effect of setting the mood, making the text lighter or more empathetic. So keep those words that are not adding to what you are communicating, but affect how you are communicating.
Avoid unnecessary explanations. If you are sure your readers know what a technical term means, don't waste time explaining it. This is tricky advice because software developers tend to err on the side of using jargon without any explanation at all, even to non-tech readers. So make sure you know your audience and can correctly assume what they know and what they don't.
Be aware of metadiscourse. Metadiscourse is the language used to contextualize each idea you are presenting in reference to the text itself. It is used to explain the order of your text: "My first argument is that..." or "The last point I want to make. is…". It is also used when you are presenting an argument and want to punctuate that something is hypothetical: "Imagine that..." or "Consider now that...". Or when you are anticipating the reader's response: "You might think that..." or "It is natural to think that...". Metadiscourse is present in almost everything we write and might be very helpful, but try not to abuse it.
One good rule of thumb for identifying excessive metadiscourse is: read it aloud, if you sound too formal, pompous, pretentious or theatrical, then you have some metadiscourse to eliminate. Aim for sounding straight to the point and clear-cut.