Does anyone else find that they "snag" fish on the dropper?

I find I can "see" the strike more often with a dry fly as my strike indicator, but I also find that I occasionally snag fish using this system.

This only seems to happen often when I'm using my dry fly and dropper

This bothers me.

What am I doing wrong?

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Swing hard, in case they throw the ball where you're swinging. Duke Snider