  We present a theoretical analysis of a novel cavity electromechanical system
where a mechanical resonator directly modulates the damping rate kappa of a
driven electromagnetic cavity. We show that via a destructive interference of
quantum noise, the driven cavity can effectively act like a zero-temperature
bath irrespective of the ratio kappa / omega_M, where omega_M is the mechanical
frequency. This scheme thus allows one to cool the mechanical resonator to its
ground state without requiring the cavity to be in the so-called `good cavity'
limit kappa << omega_M.
