Compression can bring in unwanted modulation of the high-frequency sounds.
This happens when a large amount of gain reduction happens to the signal because of high-intensity bass sounds.
Bass sounds, perceived level, actual sound energy
Bass sounds need much higher energy to be perceived as loud as a high frequency sound. We will hear a louder hi frequency sound and quieter bass frequency sound even though the energy coming out of the speakers is the same.
For a kick (bass frequencies) to be perceived as loud as a high hat (hi frequencies), the actual sound energy of the kick has to be much higher than that of the hi-hat.
Hi gets compressed along with the bass
Any high-frequency sounds that occur at the same time as high-energy bass sounds gets compressed along with the bass. This makes hi-hats and other bright sounds pulled down without we wanting it.
In most music, especially electrically assisted music, the majority of the sound energy emanates from the bass end of the spectrum, obvious examples being the kick drum, bass synth, and bass guitar.
A multi-band compressor can apply different amounts of gain reduction to different sections of the frequency spectrum. iZotope Ozone is a software effects bundle that has a good multi-band compressor. Waves C4 is another good example, which is included in the Waves Diamond Native Plug In Bundle
izotope ozone, multi-band compressor interface
In the case of hi-hats and similar percussive instruments, you can try reducing the frequency modulation problem by increasing the attack time, allowing the hi-hat to pass through. If you are able to solve the problem or not depends on how much gain reduction is being actually applied.
The sound quality of compressors differs depending on their design and the type of gain-reduction elements used. Some designs are valued for the effects they create rather than for their integrity or transparency. The shortcomings can be used as creative effects.
COMPRESSION AND NOISE
If noise is a problem, use as little compression (gain reduction) as possible.
Compressors do not introduce any noise by themselves. But…
When we apply compression on a signal, the louder parts are reduced in level by compression, depending on the ration and threshold we set. To make up for this, we raise the gain of the output signal from the compressor. Now the quieter parts of the original signal and any noise those parts may contain, will also be raised in level.
If the maximum levels of the compressed (output) and uncompressed signals (input) are kept the same, each dB of compression applied, makes the signal-to-noise ratio worse by 1dB.
Best way to remedy this is to take care of the noise in the input signal while recording. Make sure that the signal to noise ratio is as high as possible using good micing techniques, keeping the input levels high enough and using reasonably good equipment.
We can also try using a gate to cut off the low level, noisy parts which are not relevant to the mix.
Want to learn more about using effects? You may find Effective equalization useful.