To change from 1/200 to 1/1600 that’s a three-stop difference in exposure, as long as the aperture and ISO don’t change.
If you find 1/1600 to have given a good result, then you will find 1/200 to be three stops overexposed and most of the time that causes irrecoverable amounts of highlight clipping when you try to apply three stops of negative exposure compensation in post-processing.
Can you post any examples?