Ulysses magnetic field data are used to study magnetic field microstructure over the solar poles. Magnetic holes (MHs) and magnetic decreases (MDs) are found to be located at the phase-steepened edges of nonlinear Alfv¿n waves. The phase-steepened edges (directional discontinuities) occur in time-coincidence with MHs, one edge of an MD, or throughout the whole MD. These MH- and MD-related discontinuities have both rotational and compressive properties, perhaps explaining why many directional discontinuities detected in interplanetary space have non-MHD properties. The dispersive, dissipative and compressive features of nonlinear Alfv¿n waves may be important for the heating of the solar corona.