If you're writing any kind of fight or chase, get hold of little action figures or toys so you can carefully and slowly choreograph the sequence on your desk. The excitement of a scene is instantly destroyed if your reader is confused about how a character's arm got from round his enemy's neck to punching him in the liver without the necessary physical transition. Block out every move in the sequence like the director of a dance show and you'll avoid asking your characters to bend over backwards or suddenly sprout extra limbs.
Once you've choreographed your sequence, cut half of it. Then cut half of it again. Reduce every fight or chase to its essence. You want maximum impact, minimum space on the page. For every twenty moves you'd see in a fight on film, write one. But make it count. In my first draft of my first book, Jimmy Coates: Killer, the helicopter chase was twenty pages long. In the final version, it's four pages. But because it's shorter it's more thrilling, it's more memorable. It should feel like it takes up more of the book than it actually does.
Jimmy does not punch people. The knuckles of the first two fingers on Jimmy's right hand connect with his enemy's clavicle. For example. Get a diagram of the human anatomy and work out precisely the bones and ligaments that are crunching or grinding or twisting and how. Be specific not just position and action but with degree - how hard is someone hitting? How fast is someone moving? The common adjectives are too loose. Better to cut adjectives altogether and use stronger verbs. Even better, show the effects of a blow and you don't need to explain how hard it was. Show how the character feels the speed and you don't need to say it's fast.
Sometimes you want to project the mess or speed of a fight or get across that so much is happening so fast nobody can keep up. That's when you need to step back and let the reader fill in the gaps. Don't itemise every blow with the detail you would if you were being specific. This works well towards the end of a book when the reader has already imagined enough specifics to be able to know the detail instinctively when you only suggest an outline. So switch to overall dynamics. You'll need to rely a little more on metaphor and simile to make it work. This might not make much sense without an example, so here's a fight between two young would-be assassins near the end of Jimmy Coates: Power...