LM386 speaker hum

The noise doesn't seem to be at any one frequency, but rather across the spectrum, with more low than high freq component. Scope and FFT shots below. Turning the wall-blister on and off doesn't seem to affect the noise - it seems to come entirely from the amp side of things.

I'm basically using the second circuit from here:
LM386 Schematic diagrams (the one with the 200 gain), with the bypass (pin 7) grounded directly, not through a cap.