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If you are using a compressor, then you are either compressing to reduce dynamic range (the difference between loud and quiet), or just because it sounds nice, which it often does.
It doesn't matter which compressor you are using, or how you are using it, it will always make the signal more noisy.
All signals contain a certain amount of noise. Noise is generated in natural sounds in the air, in electrical signals, and in analog-to-digital converters. There is no such thing as a noise-free signal.
When a signal is compressed, the high-level sections are lowered in level, bringing them closer to the quiet sections. But that makes the peak level of the signal less and its loudness is decreased.
To correct this, the 'gain make-up' control is used to restore the levels of the peaks to what they were. In doing so, the lower-level sections of the signal are also brought up in level.
Mixed in with the signal is noise, and that is brought up in level too. During the quieter sections, the noise will be audible, and more audible than it was before.
There is one way of dealing with this if the quiet sections of the signal don't matter. That will be case if the quiet sections are actually gaps, such as the periods between lines and verses of the song.
Without further processing, it is quite possible that noise in these gaps will be loud enough to be audible after compression.
So the answer is to use a noise gate. Or edit out the gaps, making sure of course that there are no clicks at the beginnings and ends of the audio regions that will be created during this process.
It is also possible to use an expander, which is like a noise gate but a little more subtle and gentle.
It sometimes comes a surprise to someone who is just getting to grips with sound engineering that even expensive and well-designed compressors make the signal nosier. But it is an inevitable part of the compression process.