We have shown earlier that compressional magnetic fluctuations modify the properties of MHD waves. The modifications can be large even when the fluctuation level is much smaller than the ambient magnetic field. There are two kinds of effects: resonant and non-resonant. The former is a result of the so- called parametric cyclotron resonance, and enables energy transfer from the wave to particle Larmor motion. This transfer causes the damping of waves even when their frequency is so small that ordinary cyclotron damping is negligible. The non-resonant effect does not cause energy exchange, but it does modify wave dispersion and causes mode coupling between the shear Alfvén mode and magnetosonic modes.