Structure-borne sound generated by audible vibration of machines in vehicles, equipment and house-hold appliances is often a major cause of noise. Such vibration of complex machines is mostly determined and quantified by measurements. It has been found that characterization of the vibratory source strength and the prediction of power transmission to a supporting structure or the machine casing itself can be greatly simplified if all mobility cross-terms and spatial cross-coupling of source velocities can be neglected in the analysis. In many cases this gives an acceptable engineering accuracy, especially at mid- and high-frequencies. For structurally compact machines, however, the influence of cross-coupling cannot always be ignored. The present paper addresses this problem and examines the transmission of structure-borne sound power by including spatial cross-coupling between pairs of translational terminals in a global plane. This paired or bi-coupled power transmission represents the simplest case of cross-coupling. The procedure and quality of the predicted transmission using this improved technique is demonstrated experimentally for an electrical motor unit with an integrated radial fan that was mounted resiliently in a vacuum cleaner casing. It is found that cross-coupling plays a significant role, but only at frequencies below 100Hz for the examined system.