There are two schools of thought about singers moving when recording.
One says that ideally the singer should keep a constant distance from the microphone. This will keep the tonal quality of the voice consistent all the way through the recording.
The other says that the singer should employ 'microphone technique' and move closer for quiet sections, further away for loud sections of the song.
Either can be a viable approach so use what works best for you.
What doesn't work however is if the singer moves at random!
This can happen with acoustic instruments too. A moving trumpet player is about the worst it gets because the trumpet is a highly directional instrument and very sensitive to positioning with respect to the microphone.
The very best solution to a moving singer or instrumentalist is to TELL THEM TO STOP MOVING!
OK, tell them gently at first, then be more insistent if necessary.
Hopefully they will get the message and realize that the recording will be better for it.
Sometimes though, you might find that the singer becomes inhibited by not being able to move.
In this case you might get a more consistent level and tone of voice, but the singer doesn't give a good performance.
Nearly always it is better to have a great performance than have every detail technically correct in the recording.
If the singer does move, then compression is not the solution.
The solution is to use fader automation to control the level. A compressor reacts automatically and sometimes wrongly. With fader automation, you are always in control.
It might take some time to get right, but it will be time well spent.
Once you have got the level as consistent as possible, bounce the vocal to a new track. Then you can compress it any way you like.
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