With high impedance earphones plugged into the audio jack on the Kenwood TS-590S or TS-590SG, you can hear a really annoying noise even with the AF volume set to zero. This audio hiss has a constant level, is added to the audible RF noise and can prevent one from hearing weak CW signals on an otherwise quiet band.

A simple quick-and-dirty solution is a resistor in series to the audio output. With this little modification the audio hiss becomes inaudible, while all radio signals are loud and clear. Depending on the resistor value, you have to increase the AF volume more or less. Resistors with a value of 300 to 600 Ω are adequate. I personally have put in a 330 Ω resistor, as shown in the picture below. With resistors >600 Ω, you have to increase the AF volume a lot. Clipping or other kinds of audio distortion may occur.

Another simple solution is the usage of a very low impedance headphone, where the impedance has to be close to 8 Ω.

The TS-590SG In-Depth Manual states, that the audio output of the TS-590S was designed for headphones with 8 Ω impedance, which is also true for the TS-590SG, but the circuit has changed.

From the In-Depth Manual:

The TS-590SG lowers the impedance at the headphone jack to reduce these kinds of symptoms when a high impedance headphone is used. This will reduce the hissing noise by approximately 8 dB compared to the TS-590S when the impedance of the headphone is 32 Ω. In this case, increase the AF VR slightly to adjust to the same volume as TS-590S.

Nevertheless the hiss is still audible on the TS-590SG.

Adapter
Adapter with a 330 Ω resistor in a 3.5 mm audio jack