Imaging the acoustical nonlinear parameter using second-harmonic and difference-frequency waves produced from finite-amplitude sound propagation is described. Experiments for reconstructing nonlinear-parameter tomograms were performed with gelatine phantoms. The tomograms were not of high quality because we used a small-aperture receiver to detect the substantially refracted waves. We show that by laterally translating the receiver to the position of maximum intensity for each measurement of a point on a projection, we can improve the quality of nonlinear parameter tomograms as well as that of conventional attenuation tomograms. We analyze the effects of attenuation and diffraction for a narrow transmitted beam in nonlinear parameter imaging. Using second-harmonic waves is advantageous for attenuation compensation when the attenuation in the object is proportional to the frequency, such as is the case for soft biological tissue. On the other hand, using difference-frequency waves has certain advantages where attenuation is not a problem. With these waves there is less phase variation.