Thanks JohnK. I think you're saying that the only really useful measurement of "what an amp can do for you" is a distortion vs power graph - am I understanding you correctly ?
I guess what I'm wondering about is that even such a graph could deliver different results depending on how long the input signal lasted at each power level. It seems to me that there are sorta-kinda three levels that matter :
1. Continuous power -- no clipping, no overheating, no overloading devices (do I have that right ?)
2. Power at "clipping" (with the caveats you mentioned) where the test signal is long enough to drag down the power supply rails but not long enough to overheat
3. Same as #2 but where the test signal is short enough that the main power supply caps don't discharge much and so rail voltage stays high
It seems to me that "headroom" as people talk about it is probably closer to #3 than to #2, but still somewhere in between since the amp is already being driven at a lower average level which may be enough to start dragging down the rail voltages anyways.
I imagine that on some (most/all ?) powerful amps the power supply is sufficiently beefy that rail voltage drop & power supply ripple don't get too bad even at full rated power, but I'm also trying to figure out what a suitable "headroom or whatever we want to call it" rating for typical amps found in average receivers might look like.
Put differently, in big-ass amps everyone talks about headroom "over and above" the continuous power rating while for typical receivers & integrated amps you don't hear those comments (although that could obviously be a function of target audience), so being me I'm obviously trying to figure out if there really is a difference (I think there is) and if so to quantify that difference.
http://dilbert.com/strips/comic/2007-04-05/ 
