I have recently attended a Reactive Pistol course from Dr. William April. He teaches to shoot as soon as the sights reach their intended target. His justification for this is if a person is standing there, arms extended, holding their sights on target the best they can, there is a still a wobble zone. The shooter needs to ask themself are they really that much more accurate during slow fire than when they break the shot as soon as the sight align on the target. After a few repetitions of this technique, the hits were as good as I get even with the slow aimed fire.
He also taught a technique that is different than the traditional looking for the front sight, then the target and then firing. His technique is to look at the target and bring their firearm into your line of sight. This goes for putting shots on one target and even applies to transitions. His technique was to snap your head to the next target and then your sights would follow into your line of sight. This was working well for me for a while, until my shots were consisting landing high. Dr. Aprill diagnosed that I was probably not using my rear sights. After his further explanation of looking through the rear sights as a window, then I brought my shots back down onto target. After more and more dry and live fire on my own since, it really impresses me how the sights seem to find their way to the target when I am focusing on the target and snap the sights into my line of sight. They are consistently on target or very close with minimal adjustment needed before breaking the shot.
I have recently been reading Bullseyes Don't Shoot Back, written by Col. Rex Applegate. He studied under William E. Fairbairn and E.A. Sykes. They were English police that worked in Shanghai between 1900 and 1940, when the city was one of the most lawless in the world. Col. Applegate talks about the technique that Wild Bill Hickok used. Hickok received a question in writing asking how he killed all those men. He wrote back, "I raised my hand to eye level, like pointing a finger, and fired." This was contrary to all the Old West shoot from the hip that was portrayed on tv.