When using a pistol/handgun, just bringing it up to target works (for me at least).
You still need to find the sight no matter which way you go and getting it on target as fast as possible is key, thus, bring to aim, focus on the front sight only and squeeze the trigger, don't pull it. Once the trigger breaks, hold it back for a second (called follow through), then release for the next shot.
The reason for follow through is because quickly releasing the trigger will affect your shot due to the extra movement if releasing immediately.
My 2¢.

mike