Measuring of AM/AM conversion of a PA

I thought that one can measured the am/am conversion of a PA by changing the input power and measuring the output power (with a spectrum analyser...). By I read that one can also measured it with an AM modulated signal (with low modulation index) at the input and see how the modulation index is transformed. I'm a little bit trouble because for an AM modulated with a constant index modulation,the signal average power is constant (not changing)!
Perhaps, I misunderstang some thing!
Another question with using a low modulation index? Is it for Harmonic issue?

Thanks for your helps

It is and is not constant power. If you hook up a power meter to an AM modulated carrier, it reads a constant value. But if you hook up a fast detector, like watching the envelope on a fast oscilloscope, you will see that the power is changing from microsecond to microsecond. In this case, the power meter is acting like an "average power" meter.

I would be a little careful about trying to equate quick AM Modulation supression measurement to a standard 1 dB output power compression point measurement. It has long been known (Routhroth) that you can be fully compressed, and still pass significant AM modulation. That is why an amplifier that is quite compressed does not really strip off much AM noise! They really are not 1:1 related, but depend a lot on device physics, etc.

So you agree to say that the am-am conversion is linked to the PA compression! and the more compressed the PA is the lower is its AM/AM conversion?