A new imaging sequence for rapid determination of the apparent self-diffusion tensor of water was developed and tested on fixed excised rat spinal cords. To reduce the time required to determine the tensor, the sequence utilized a new single-shot approach with multiple spin echoes. An assumption of cylindrical symmetry in the sample was made, thus requiring the measurement of only four of the six unique elements of the tensor. This assumption was found experimentally to be valid, and the results obtained using the new sequence were found to be quantitatively the same as results obtained using a standard spin-echo sequence.