Want to get more out of your compressor? Combine its sidechain input with an equalizer! (Some compressors have filtering and/or EQ available as built-in processing on their sidechain inputs.)
Running the signal coming into a sidechain input allows you to make the compressor more sensitive to certain frequencies or a range of frequencies. For example, a compressor can be turned into a de-esser by running the sidechain input signal through an EQ and boosting the high freqencies. Likewise, the compressor can be used to tighten up the bass range by boosting the low frequencies of the sidechain input signal.