You'll often hear people say that you should always cut before you boost when using an EQ.
While I agree somewhat with this concept in the analog world, as boosting really limits the headroom on a channel, there is another reason this theory has made its way into many textbooks and classrooms on EQ. Since each harmonic has a distinct pitch, not all harmonics are musically related to the fundamental in a way that is pleasing. So decreasing these harmonics can clean up the sound and make the sound much more pleasing to listen to.