With high impedance earphones plugged into the audio jack on the Kenwood TS-590S, 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. With the 1 kΩ resistor shown below, you have to increase to AF volume a lot. Clipping or other kinds of audio distortion may occur. Resistors with a value of 300 to 600 Ω are adequate. I personally have put in a 330 Ω resistor.
Another simple solution is the usage of a very low impedance headphone, where the impedance has to be close to 8 Ω.