It has previously been shown that the attenuation of ultrasound (US) by microbubble contrast agents is dependent on acoustic pressure (Chen et al. 2002). Although previous studies have modelled the pressure-dependence of attenuation in single bubbles, this paper investigates this subject by considering a bulk volume of bubbles together with other linear attenuators. Specifically, a new pressure-dependent attenuation model for an inhomogeneous volume of attenuators is proposed. In this model, the effect of the attenuation on US propagation is considered. The model was validated using experimental measurements on the US contrast agent Sonovue. The results indicate, at low acoustic pressures, a linear relationship between the attenuation of Sonovue, measured in dB, and the insonating acoustic pressure.