The original question was how to decrease power supply noise, but after discussion it seems to be just a measurement problem.
Case 1: When I short the ground lead to the probe, I read about +-2mV rms - acceptable by me. Case 2: When I connect the ground lead and the probe to the 0V of the power supply, I get a lot of noise with spikes up to +-50mV - not acceptable.
Common sens and several people say that in both cases, I should have a reading as in the case 1. What could be wrong with the oscilloscope?
The oscilloscope has an earth ground pin in the AC power cord. The power supply also has the ground pin in its AC power cord. I do not connect power supply's negative negative terminal to the earth ground (the green connector on the front panel). Even if I do, it does not seem to affect the measurement - I still get the same random noise.
Please, help me to find the source of this noise.