The magnetic fields measured by the Ulysses spacecraft are used to study solar wind turbulence in the fast solar wind from the south polar hole. The spacecraft was at about 46 deg south latitude and 3.9 AU. For a magnetic field with a Gaussian distribution the power spectrum (second-order structure function) is sufficient to completely characterize the turbulence. However, the actual distribution is non-Gaussian so that the effects of intermittency must be taken into account. The observed spectral exponents include effects of intermittency and cannot be directly compared with the standard second-order spectral theories such as the Kolmogorov and Kraichnan theories. To permit a better comparison of the observations with the theoretical models, we study the structure characteristics of the data. We find the exponents of the second-order structure functions (power spectra) and the higher-order normalized structure functions for the components of the magnetic fields. We show that these sets of exponents can be approximately described by two basic numbers: the spectral exponent and the intermittency exponent. The intermittency exponent characterizes correlation properties of the energy cascade from large to small scales. Before comparing the observations to the theoretically expected values, a reduction must be made to the observed spectral exponent. The amount of the reduction depends on both the intermittency exponent and the model of the energy cascade assumed in the turbulence theory. We reduce the measured spectral indices according to a simple model for Alfv¿n turbulence that is described here. We then compare our reduced spectral indices with second-order spectral theory. The reduced spectral indices for the period range of 1 min to about a half hour are remarkably constant and in good agreement with the value of 3/2. Thus our treatment is self-consistent. Our tentative conclusion is that the high-frequency turbulence appears to agree with the model of random-phased Alfv¿n waves. This tentative conclusion must be tested by further theoretical and observational work. ¿ American Geophysical Union 1995