Push-Pull Along The Rail
When you have to make a fast, accurate first shot, details matter.
Whether you're trying to win a competition, max a qualifier, or stop a threat, accuracy and fractions of a second count.
It takes the average shooter .25-1 second to converge their focus from their target to their front sight, depending on the person and the distance to the target.
If your sights are already lined up when your eye gets focused, then you're good to go, otherwise you're going to have to spend precious time finding your front sight, lining up your sights, possibly re-aligning them on the target, and then focusing on your front sight.
That's a lot to do when you're under stress and pressed for time.
And that's why it's so important to have your sights already lined up on target as quickly as possible after you clear your holster.
What you want to do is imagine yourself holding your pistol at full extension with your sights aligned on a target.
Gradually pull your pistol 8-12 inches towards your eyes while keeping your sights aligned on your target, as if there is a rail going from your dominant eye to your target and your pistol sights are rolling along the rail.
Once you've pulled in 8-12 inches, push back out. This is called "Push-Pull Along The Rail," and if you practice it on a regular basis, it will make you a much faster shooter.
From now on, as you're drawing or extending your pistol from a compressed hold, try to get your sights "on the rail" as soon in your drawstroke as possible.
When you bring your pistol back in from full extension, consciously keep it "on the rail" for as long as possible.
Do this with live fire, dry fire, and when you visualize yourself shooting.
Pretty soon, you'll find yourself in a situation where you have to rush a shot, converge your eyes from your target to your front sight while you're still extending, see that you're in perfect alignment, and release an accurate shot before you even reach full extension.