What Z precision is needed for laser engraving?

Hi
I have a laser-cut and folded sheet metal box where I want to add text over some connectors.

We had it power coated and started with the CNC, trying to engrave the text. It turned out to be not possible. The engraving depth is 0.1mm, and after the folding, the case is not rigid and flat enough for this tolerance. It has 0.2-0.5mm differences.

I am thinking about buying the 10W laser and try to use that (the small laser is not strong enough for the black power coating), but I’m not sure if the changes in the case (which would translate to changes in the laser focus) would cause the same issue? How precise the laser should be? Can it tolerate 0.3-0.5mm changes on the subject?

Thanks

The height variance is a bit forgiving, so 0.2-0.5mm is fine. I’ve done slightly curved and tapered surfaces with the 10W. Considering they boast 8mm basswood cut in 2 passes, I would say you have a window of 2-3mm of near full strength (1-1.5 on either side of the focal point).