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The Nakagami distribution was recently proposed as a generalized model for the envelope of the backscattered ultrasonic echo from tissue. The parameters of the Nakagami model were also shown to be useful in tissue characterization. This paper explores the possibility of enhancing the ability of these parameters for tissue characterization through the techniques of diversity and compounding. Frequency diversity has been used to create multiple versions of the envelope, which are then combined. This compounded envelope has been modeled, and its parameters have been analyzed. The ability of these new parameters to enhance tissue characterization is studied using computer simulation and experiments on tissue-mimicking phantoms. Results indicate that the use of frequency diversity and compounding may indeed improve the ability of the parameters of the Nakagami model to separate different number densities of scatterers. Therefore, it is suggested that such an approach may lead to better techniques in ultrasonic tissue characterization.