3D ultrasound is an emerging diagnostic technique that extends standard ultrasound imaging by capturing volumes, instead of planes. This brings completely new diagnostic opportunities, among which the possibility of disjoining image acquisition and analysis, thus enabling remote diagnosis, which would bring obvious medical and economic benefits. Unfortunately, 3D ultrasound is several orders of magnitude more computationally complex than 2D imaging. Therefore, algorithmic improvements to simplify the processing are mandatory in order to conceive cheap, portable, low-power imagers. The kernel of the 3D imaging process, called beamforming, consists essentially of computing delay and apodization profiles. We have previously devised an approximation of the delay calculation stage, which dramatically reduces hardware complexity. Unfortunately, this approximation introduces an intrinsic degree of inaccuracy that can be characterized as added image noise. In this paper, we identify an efficient approximated approach to the calculation of apodization profiles, that additionally minimizes (-76%) the error introduced during delay calculation. Together, these two techniques enable an efficient computation of 3D ultrasound images.