||In this paper, we address the problem of evaluating the acoustic attenuation of "difficult" media, i.e. highly attenuating and scattering media. In a broadband, through transmission setup, the signals acquired from such media are characterized by a poor signal-to-noise ratio. Therefore, an accurate estimate of attenuation cannot be obtained from a single measurement, but multiple measurements must be combined. Two methods are considered to yield a single estimate of attenuation from multiple measurements. The first one, the "average attenuation" (AA) method, consists in a simple average of individual attenuation estimates. The second one, the "cross spectrum" (CS) method, is based on a system identification approach. In order to evaluate the estimation errors for these methods, ultrasonic signals transmitted through a material of known attenuation were simulated and mixed with both coherent and incoherent noise. In all tests performed, the "CS" method was found to yield the most accurate estimate. This method, combined time delay compensation, is then applied to real signals measured from a concrete slab. A valid frequency band for the attenuation estimate can be defined based on the coherence function. Results from this research are being applied to characterize the degradation of concrete structures using high-frequency ultrasound.