This study examines the structures of a set of rotational discontinuities detected in the solar wind by the ISEE-3 spacecraft. It is found that the complexity of the structure increases as the angle &thgr; between the propagation vector k and the magnetic field decreases. For rotational discontinuities that propagate at a large angle to the field with an ion (left-hand) sense of rotation, the magnetic hodograms tend to be flattened, in agreement with prior numerical simulations. When &thgr; is large, angular ''overshoots'' are often observed at one or both ends of the discontinuity. When the propagation is nearly parallel to the field (i.e., when &thgr; is small), many different types of structure are seen, ranging from straight lines, to S-shaped curves, to complex, disorganized shapes. ¿ American Geophysical Union 1989