In certain embodiments, a robotic attacher retrieves cups from the right side of an equipment area located behind a dairy livestock and attaches the cups to the teats of the dairy livestock in sequence. The sequence comprises attaching a first cup to the right front teat, a second cup to the left front teat, a third cup to the right rear teat, and a fourth cup to the left rear teat. In certain alternative embodiments, the robotic attacher retrieves cups from the left side of the equipment area, and the sequence comprises attaching a first cup to the left front teat, a second cup to the right front teat, a third cup to the left rear teat, and a fourth cup to the right rear teat.