I am getting a groaning sound from my right rear brake. Not all the time, but very often. Here are the symptoms:

When it happens, it begins when the brake pedal is touched gently, during the first inch or so.
It goes away when the pedal is fully depressed beyond the 'one-inch zone'.
If I ride the brake in the one-inch zone, I can keep the groan going for a few seconds.
It doesn't sound like pads on the rotor.
I took everything apart and inspected. Didn't see anything unusual.

I changed the pads and rotors recently. The sound didn't start right after that. There was a track day in between the new pads/rotors and the onset of the problem.

Thoughts anyone?