Reducing air conditioner compressor vibration noise

I have a two year old Carrier air conditioner with an outdoor condenser. The condenser sits on a plastic pad on the side of my house, and I have two–one for downstairs and one for upstairs.

Recently, the larger of the two (for upstairs) has been making an oscillating vibration noise–not too loud, but loud enough to be annoying when running. If I place my hand on the top of the unit and press down with very little force, the noise stops. Therefore, I deduce that this is a vibration problem with the metal grill that surrounds the condenser fins–maybe.

The unit was out of level, so I leveled the pad, and it sounds the same. However, with the pad level, the unit itself is still out of level and wobbles if pushed. It isn’t bolted down to the pad, as I can easily move it around. Is it not required to be bolted down?

I plan on doing the following. Does it make sense:

1. Level the condenser on the pad, with rubber for shims.
2. Remove the top fan grid (with fan attached) to see if I can place some pieces of rubber where the top lays on the condenser fins.
3. Make sure all screws are tight.

Any other ideas? (I’m a homeowner, not a professional.) Thank you.