A new general algorithm for room acoustic prediction is presented. The algorithm, based on approximate cone tracing, handles diffuse reflection by a splitup of cones incident on diffusing surfaces. The splitup of cones treats the interaction between specular and diffuse reflection in a physically sensible manner. A ‘‘brute-force’’ implementation of such an algorithm inevitably creates an exponential dependence of the calculation time on the number of reflection combinations between diffusely reflecting surfaces, and therefore results in extremely long processing times. By exploiting the properties of diffuse reflection, the described algorithm displays an essentially linear dependence resulting in processing times short enough also for personal computers. The algorithm adapts its behavior to the properties of each specific environment, relies on very few nonverifiable assumptions, and is designed to meet the specific requirements of auralization. The splitup of cones creates a myriad of weak diffuse reflections resulting in a very smooth late decay. The algorithm is described in detail and sample predictions are shown.