On some devices the screen quickly flashes once when the power button is pressed, then the animation is played.

[ds84182]

This problem could possibly be resolved by keeping a black overlay on the screen after the screen turns off. This will make sure that when the screen on animation plays, that the screen is completely black.

[ds84182]

Actually this may just be a problem with the Moto X, since Active Display keeps the screen powered. I've noticed that every time it happens the screen is extremely dim.