Had an extended play on the K2 this evening enjoying 10m :-). Noticed a birdie on 28.020 and traced it to rig control. It sounds like a tone which dies in strength when the software polls the radio for frequency etc. It's easily identified by varying the software polling rate on the computer. The tone makes an appearance on discrete frequencies on most bands above 30m. There is an extract in the K2 manual on how to disable the square wave signal generator in the rig and instead use the timing source derived from the computer. Unfortunately this seems only to apply to the KIO2 unit and not the one integrated in the KPA100. I'll have to do some web research on how to eliminate it.
While I was at it, I disconnected the antenna and tried to find any noise from my Alinco DM-330MW SMPS. Sure enough I came across a low squirming warble noise on a discrete frequency and was able to move it about with the noise offset knob on the front panel. The noise isn't really a problem for me, it's remembering to try and shift it on the PSU before QSYing.