The rate of occurrence of interplanetary discontinuities (ROID) is examined using Ulysses magnetic field and plasma data from 1 to 5 AU radial distance from the Sun and at high heliospheric latitudes. It is found that there are two regions in interplanetary space where the ROID is high: in stream-stream interaction regions and in Alfven wave trains. This latter feature is particularly obvious at high heliographic latitudes when Ulysses enters a high speed stream associated with a polar coronal hole. These streams are characterized by the presence of continuous, large-amplitude (ΔB/I Bl -1 -2,) Alfven waves and an extraordinarily high ROID value (~ 150 discontinuities/day). In a number of intervals examined, it is found that (rotational) discontinuities are an integral part of the Alfven wave: they represent -90° phase rotation of the wave out of the full 360° rotation of the wave. These large amplitude nonlinear Alfven waves thus appear to be phase steepened. The nonlinear Alfven waves are spherically polarized, i.e., the tip of the perturbation vector resides on the surface of a sphere (a consequence of constant |B|). The best description of this wave plus discontinuity is a “spherical arc polarization”.