Set triggers are out of favor from accuracy shooters because of this very type of issue. basically, a set trigger uses a tiny "hammer" of sorts to knock loose the main sear, releasing the striker. It is a click, then another click. No matter how fast this occurs, lock time is very important, and set triggers by design have slower lock times than, say, a Jewell.
That said, set triggers are VERY cool, and there are some fine, accurate examples still manufactured.