An optimal three-dimensional (3-D) coefficient tree structure for 3-D zerotree wavelet video coding is considered in this paper. The 3-D zerotree wavelet video coding is inspired by the success of the two-dimensional (2-D) zerotree wavelet image coding. Existing 3-D zerotree wavelet video codecs use the either symmetric or symmetric-alike 3-D tree structure, which is a straightforward extension of the symmetric 2-D tree structure in the zerotree wavelet image coding. In this paper, we show that the 3-D zerotree coding does not need to be applied symmetrically along all the directions, as the 2-D zerotree image coding does. We find that an asymmetric 3-D tree structure working with a more flexible asymmetric 3-D wavelet transform can produce a higher compression ratio than traditional symmetric approaches. The new 3-D tree structure can be used to improve the rate-distortion performance of many existing 3-D zerotree wavelet video codecs without sacrificing other features such as scalability and computational efficiency. The new tree structure is applied to the 3-D set partitioning in hierarchical trees method and receives convincing peak signal-to-noise ratio improvements in experiments.