We present a new ray tracing approach to volume rendering in which the low-albedo volume rendering integral for each ray is efficiently computed to any prescribed accuracy. By bracketing the emission and absorption functions along each ray with adaptively refined step functions, computation is directed toward large sources of error and continued until a desired accuracy is reached. As a result, coarse approximations can be used in regions that are nearly uniform, of low emission, or of low visibility due to absorption by material closer to the eye. Adaptive refinement for each ray is performed using a hierarchical organization of the volume data; at each step, a part of the ray estimated to contribute large error is refined, and the approximate integral is updated incrementally. Our current implementation operates on regularly-spaced data samples combined with trilinear interpolation; however, the concepts described apply to more general data topologies and reconstruction filters.