Causes of high 2nd order harmonics (tweeters)?

Hey guys,
A few years back I acquired some tweeters of the same make/model. All display low harmonic distortion, except for one. Right around resonance its 2nd order harmonic disortion shoots for several percent.

Its frequency response, impedance and CSD appear normal compared to the others.

I've considered it might be voice coil rub, but isn't that usually recognized by high order harmonics?
Correct, rub usually gives rise to all harmonics.

It could be that the soft parts have sagged and voicecoil is sitting too far in or out of the gap - this will give higher even order harmonics (lots of 2nd, a little bit of 4th, even less of 6th etc)
Thank you for replying. I wanted to provide more information in the form of distortion plots. The distortion increases greatly as the output level is increased below 6kHz.
The graphs can be viewed full-zise by right-clicking an image and selecting "view in new window" or open link in new tab".

Sweep 1kHz - 10kHz, distortion values in the legend refer to 2.25kHz:

1kHz Pure Tone:

2.5kHz Pure Tone:
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That looks like coil rub.

The distortion profile contains every harmonic and it seems to happen with stimulus up to 7kHz (based on your first graph). If this were a suspension issue it would only happen in a narrow range.

If you can take the driver apart, check the gap for a small piece of debris. If nothing is in there, use your judgement to move the coil assembly a very small amount in the opposite direction and put the speaker back together. Some drivers have provisions in the top plate for rotating the entire magnet in increments for this very reason.