The present invention provides means of enhancing the acoustic attenuation and vibration damping of a material by (1) embedding a plurality of small particles of either a high characteristic acoustic impedance or a low characteristic acoustic impedance or combinations of high and low characteristic acoustic impedance materials to form a matrix material to act as a acoustic attenuator or vibration damper; and (2) combing this matrix material with a second layer of a decoupling material that serves to effectively isolate the matrix material and reduce its tendency to vibrate sympathetically to the impinging acoustic energy. The mass of the resultant material may be very low while retaining excellent acoustic attenuation, vibration damping, and structural characteristics.