In this paper we show that one can measure integrated attenuation for a soft-tissue structure simply by measuring the center frequencies of the incident and transmitted pulses. Except for a multiplicative constant, the integrated attenuation is equal to the difference of these two frequencies. Also, this method is independent of transmittances at tissue-tissue and tissue-couplant interfaces. Since the attenuation information is derived from frequency shifts rather than the signal amplitudes, this new method is somewhat insensitive to a partial loss of signal caused by beam refraction. This technique is based on the power spectra of transmitted ultrasonic pulses approximating Gaussian functions. The validity of this approach has been checked by computer simulation. Tomographic reconstructions of the experimental data using the various attenuation measurement techniques are presented.