Recent physiological studies coupled with intracellular staining have subdivided ON directionally selective (DS) ganglion cells of rabbit retina into two types. One exhibits more “transient” and more “brisk” responses (ON DS-t), and the other has more “sustained’ and more “sluggish” responses (ON DS-s), although both represent the same three preferred directions and show preference for low stimulus velocity, as reported in previous studies of ON DS ganglion cells in rabbit retina. ON DS-s cells have the morphology of ganglion cells previously shown to project to the medial terminal nucleus (MTN) of the accessory optic system, and the MTN-projecting, class IVus1 cells have been well-characterized previously in terms of their dendritic morphology, branching pattern, and stratification. ON DS-t ganglion cells have a distinctly different morphology and exhibit heterotypic coupling to amacrine cells, including axon-bearing amacrine cells, with accompanying synchronous firing, while ON DS-s cells are not coupled. The present study shows that ON DS-t cells are morphologically identical to the previously well-characterized, “orphan” class IIb1 ganglion cell, previously regarded as a member of the “brisk-concentric” category of ganglion cells. Its branching pattern, quantitatively analyzed, is similar to that of the morphological counterparts of X and Y cells, and very different from that of the ON DS-s ganglion cell. Close analysis of the dendritic stratification of class IIb1 ganglion cells together with fiducial cells indicates that they differ from that of the ON DS-s cells. In agreement with one of the three previous studies, class IIb1/ON DS-t cells, unlike class IVus1/ON DS-s ganglion cells, in the main do not co-stratify with starburst amacrine cells. As the present study shows, however, portions of their dendrites do deviate from the main substratum, coming within range of starburst boutons. Parsimony favors DS input from starburst amacrine cells both to ON DS-s and to ON DS-t ganglion cells, given the similarity of their DS responses, but further studies will be required to substantiate the origin of the DS responses of ON DS-t cells. Previously reported OFF DS responses in ON DS-t cells, unmasked by pharmacological agents, and mediated by gap junctions with amacrine cells, suggests an unusual trans-sublaminar organization of directional selectivity in the inner plexiform layer, connecting sublamina a and sublamina b.