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The paper is focused on sound-speed image reconstruction in 3-D ultrasound transmission tomography. Along with ultrasound reflectivity and the attenuation coefficient, sound speed is an important parameter which is related to the type and pathological state of the imaged tissue. This is important in the intended application, breast cancer diagnosis. In contrast to 2-D ultrasound transmission tomography systems, a 3-D system can provide an isotropic spatial resolution in the x-, y-, and z-directions in reconstructed 3-D images of ultrasound parameters. Several challenges must, however, be addressed for 3-D systems-namely, a sparse transducer distribution, low signal-to-noise ratio, and higher computational complexity. These issues are addressed in terms of sound-speed image reconstruction, using edge-preserving regularized algebraic reconstruction in combination with synthetic aperture focusing. The critical points of the implementation are also discussed, because they are crucial to enable a complete 3-D image reconstruction. The methods were tested on a synthetic data set and on data sets measured with the Karlsruhe 3-D ultrasound computer tomography (USCT) I prototype using phantoms. The sound-speed estimates in the reconstructed volumes agreed with the reference values. The breast-phantom outlines and the lesion-mimicking objects were also detectable in the resulting sound-speed volumes.