While they are known by many names, I call them rhythm drills.
A rhythm drill is nothing more than firing a certain number of rounds at a target, in a rhythm or "cadence". As you get used to the rhythm you fire at, you speed it up.
You can start out with 3 rounds, and jack it up to how ever many you want.
1. BANG...... BANG...... BANG
2. BANG.... BANG.... BANG
3. BANG.. BANG.. BANG
4. BANGBANGBANG
Rhythm drills allow you to identify and adjust deficiencies in your fundamentals, and show you what an acceptable sight picture looks like at a given range, for a given sized target, at a given speed.
You can make adjustments to your stance, grip, aiming technique (either sight picture or sight alignment), and trigger manipulation or follow through and pretty much immediately "feel" or notice a difference. Once you find your "sweet spot" you can really start pushing yourself, OR move to another range or change the size of your target.
Analyze your shot group to determine if you need to speed up or slow down. Push yourself for speed, but find that fine line between speed AND accuracy. That is up to YOU to decide.
Aside from live fire, dry fire regularly. While you NEED to live fire to improve, dry fire will help you develop the right mind set / focus, and can help speed up those things that eat up time in a stage like mag changes / draws etc...
Look at your equipment as well. I shoot .45 CDP and single stack, but I KNOW that I can fire faster with a smaller cal weapon. If you want to be as fast as possible, you have to accept that it MAY be easier to shoot something that is easier to control. Check out your loads too. Reloading your own ammo may help your recoil management if you are currently using rounds that are way over power factor.
Bottom line: to be the best requires natural ability, dedication, training, and good equipment.
Assess what you have, and keep in mind that dedication and training can go a long way to make up for deficiencies in both natural ability and equipment.