[Amps] Slow start-up of Amps on CW

[Jeff in Mali:]

Dear All:
I find that on CW, I miss the first letter or two letters of people's call. I thought that it was just me not paying attention or half-deaf from too many years cutting grass as a kid with lawn-mowers with no mufflers. 
However, more and more I'm convinced that some amps are not instantaneous, not picking up immediately as the first letter(s) is (are) keyed on CW or spoken on SSB. The other night I was watchin my own amp (Elecraft KPA-1500) and it seemed only to come up to full-power after a few characters.
Is this a generalized phenomenon, or just my imagination?
73, 
JeffTZ4AM/K1MMBBamako, Mali