Almost every tactical school or course I ever attended this principle was expressed: "Smooth is fast, Slow is smooth; therefore, slow is fast." At first glance this saying seems like a contradiction. It is more of a paradox if you will. The concept is very simple, but very hard to put into practice, especially under stress. This saying can apply to all avenues of life, but we will confine it to the area of pistol shooting for this piece.
Being smooth is being clean, direct and efficient in your movement. This is most often applied to the handgun draw and presentation to the target. (It can be applied to all tactical disciplines) While mastering the draw, most shooters are so focused on being the fastest draw, that they make extraneous movements due to the frantic rush that ends up adding steps and movement to their draw. The idea is to start off slow and methodical, build the movement memory (muscle memory) and be consistent in your repetitions. This will grove out a direct path to the draw and create smoothness in the movement. After some serious conditioning, the movement becomes intuitive and speed can be applied along the trained movement. Just like anything in the life, the more you practice the better you get and therefore can add more speed until the movement starts to break down. At that point you can slow back down, return to smoothness and slowly add more gas. It is an on going process of refinement.
Using the above principle, you can slowly and effectively push the level of your proficiency up in any activity. Since we are dealing with the personal defense aspect of skill development, this type of training could one day save your life, not to mention it is fun improving. Stay Safe!