When I go to the range I usually have some goals for what I work on, something like dot torture for accuracy and the 5x5x5 drills for speed.

If I want to work specifically on shooting faster while retaining acceptable accuracy, what are the best drills?

Basically, do I just need to make a good sight picture, fire, make a good sight picture, fire, and keep repeating as quickly as I can?  Or is there something more I should be doing?

Thanks!

There are tons of Handgun drills

Bill Drill or Bill Drill 2 are great ones for developing speed.

Karl Rehn and John Daub developed a table for Grand Master Par times at various distances:


Ben Stoeger's Practical Shooting Training has some detailed advice for developmental paths, drills, and standards.

I have found that unconventional means like airsoft and point shooting are helpful.  You can shoot and airsoft pistol faster than a firearm, which acts as "overspeed training".  Proper point shooting techniques develop a proper "look and feel" that also helps with sighted shooting speed.

From what I have found the more you draw and fire (if you're doing it right)  the better you get.
Also, finding several drills that work for you and switch them up.  Don't do the same drill for months on end.  Do it till it feel you've got it, do it a bit more then switch up to something new for a bit, then go back or on to another.

I think my favorite drill that I can see improvement from if ran a lot and regularly is called the "Fast Drill"...  
You have an 8.5x11 piece of paper.  On it is a 3"x5" (like an index card) then below it is a 6-8" circle...

Actually, I think its supposed to be printed on 8.5x14, so 8.5x11 makes it a bit smaller and harder...
Either way, I enjoy this on...

I'll take a half dozen mags, a box or two of ammo, my timer and targets, go out in the back yard/range and run it as many times as I can with the ammo taken.

The F.A.S.T. (Fundamentals, Accuracy, & Speed Test):
Range: 7 yards
Start position: weapon concealed or in retention duty holster with all retention
devices active; shooter facing downrange in relaxed stance with arms down at
sides.

Drill begins from the holster, pistol loaded with exactly two rounds.
draw
fire two (and only two) rounds at the 35 box
perform a slidelock reload
fire four (and only four) rounds at the 8 circle

***I will sometime do it in reverse, starting with the 4 shots to the circle, then two to the 3x5 box.  Sometime without a reload.
Sometimes with reload, but I have a friend load 5 or 6 mags, with a Snap cap or two randomly inserted to where I have to clear them.
Sometimes one handed, sometimes weak handed. Also tried from behind cover (a plastic barrel or sheet of plywood)  and from the ground using a laser and not using a laser***
As a Bonus, do it Suppressed.  It changed the way your pistol handles...   For even more fun try it with a rifle or PCC!!!
You can switch it up, make it fun and keep it fun!!!!

Scoring:
Opentop retention (ALS, SERPA) without concealment
add 0.50 seconds to the final score.
Flap/retention mag pouch subtract 0.50 seconds.
Misses to 3x5 box add 2.00 seconds per miss.
Misses to 8" circle add 1.00 seconds per miss.

Ranking:
10+ seconds: Novice
less than 10 seconds: Intermediate
less than 7 seconds: Advanced
less than 5 seconds: Expert

Link to the printable .pdf file. On PistolTraining.com's site.

Practice cadence shooting opposed to using a perfect sight picture to dictate when to shoot.  

Setup a 3-4" target zone and start at 3-5y.  5 shot strings. Start counting off in your head with "One one-thousand, two one-thousand, etc"... firing on the one, two, three, four, five.  Then do "one and two and three and four and five"... firing on just the numbers again. Then do "one and two and three", firing on the numbers and the "And".  Next "One, two, three, four, five" as fast as you can if you're still keeping all on target but might be missing by now.

Work up speed, increase distances, figure out when the wheels fall off and where your cadence needs to be to maintain acceptable accuracy based on target size and distance.   Watch the sight drop back onto target under recoil, figure out which angle it's coming from, fix your grip to get it recoiling vertically or at least know how it's recoiling.  Work on timing the shot early as the front sight or dot approaches reentry into the top of the circle because it is being fired while  the muzzle is in motion.

Shoot steel.  A lot of steel.  Instant feedback.

Shoot far steel, then shoot near steel.

Then shoot more steel.

I hit a wall many years ago and came up with these:

B8 center on USPSA
5 rds at 5,10,15,20 and 25. No par times on strings
Works accuracy outside 8 ring is minus 10. 250 possible

Same drill with par times of 4,5,6,7,8 seconds near to far
Speed and accuracy. 225 is 90%

USPSA target
5 rds at 5,10,15,20 and 25 no par times
Time each string and add them up. Anything outside A zone is plus 5 seconds

6x6x6
USPSA target
Shoot 6 at .25 split,6 at .50 and 6 at 1.0 at 5 yards
Analyze group size and memorize. Tape and shoot next six.
Repeat at 10,15,20,25 yards
Use timer to confirm mental count for splits.
.25-“1,2,3,4,5,6”
.50-“1 and 2 and 3 and …”
1.0-“thousand 1, thousand 2….”

Track gun after shot develop technique so that it lifts at 12 o clock and flatten it out for recovery to POA. Learn to jerk trigger. Make shot break on the count regardless of where it is pointing (unnatural act). To shoot fast you have to shoot at a tempo and learn to control it at a given speed. Increasing one split time to regain control with accuracy as your emphasis will deprive you of the opportunity to learn. Speed shooting is about consistent technique for control and predictable lift and recovery. Get physical on the gun. Those of use who where trained in the classic fundamentals were let down and those habits hold us back. You cant stabilze the sights between shots, press to a surprise break etc to shoot .25 or less splits. The sights will always have some movement at speed. Learn when you shoot with target focus and when you cant. Techical vs acceptable shots. Focal shifting takes time and increases splits. There is more of course when i teach but this is the basis.

When measuring only speed use steel. The size of the steel defines the standard or acceptable accuracy requirement. Ie A zone steel etc. paper for accuracy snd planned exercise for paper to diagnose issues when shooting speed. Need to see where the miss is to make adjustments.

Train on a conscious level so later these become subconscious acts. Look up Four Stages of Competency

Set up near to far arrays based on known shooting solutions from 6x6x6 and count you splits through it, transition to transition

This statement makes me think you need more polishing on the basics. Here’s why, when you present your pistol you shouldn’t need to “make a good sight picture” you should only be confirming it. Secondly when you fire and the pistol returns, you should again only be confirming and the sights should return to right about where they started. If this is not happening then your fundamentals are breaking down somewhere in the cycle.

Indeed.