One thing I've noticed lately is that a lot of players struggle with speed control when it comes to safety play. I was shown a drill by Jerry Briesath, whom I consider to be the best instructor that ever lived, that I've been teaching to my students. They love it because it really helps them understand how critical speed control is.
Spread out all 15 balls on the table. Take cue ball in hand on the first shot only. You lag the cue ball to any object ball, with the object being that after contact, the distance between the cue ball and object ball is no more than 4-6 inches. You can start out with 6 inches, but try to keep it at 4 or less. Also, you don't want to pocket a ball, so if a ball is near a pocket, you may have to hit it on an angle. The challenge is still to keep them within 6 inches of each other after contact. You are not allowed to shoot the same ball twice in a row. Done properly, you could do this drill for a long time without failure. Do the drill at least until you feel like you have the speed down pat.
The purpose of the drill is not to play safe, but to get a better understanding of which speed to use when certain situations come up.
One thing that students begin to understand quickly is that this shot requires an extremely short stroke, and that is something that few students have taken the time to master. This shot requires a stroke that is only an inch or two long. Some players will cue closer to the object ball, some will use a normal bridge. It's personal preference, but the key is to keep the stroke really short. I keep my bridging distance the same, but use a shorter stroke.
Depending on the initial distance between the cue ball and object ball, you may have to follow through a little bit. Still, the follow-through will be minimal because you don't want the object ball to move very far after contact.
It's all about learning different speeds, and how much or little acceleration you need in your stroke.
This shot works best if the cue ball and object ball are straight on. The diagram illustrates how you benefit from this knowledge and from mastering this stroke. Over time you develop the proper touch, so even if you have to go one rail to land on the object ball, you know the proper speed.