During the outbound pass of the Jovian magnetosheath in February 1992, a large number of magnetic depressions, without a significant change in the direction of the magnetic field vector, were observed by the Ulysses magnetometer. These low‐frequency fluctuations, identified earlier as mirror mode waves, lasted about 1 day. The largest amplitude fluctuations (with a decrease in the field magnitude by a factor 3, on average) were observed just after the spacecraft crossed the magnetopause. The amplitude of the waves decreased as Ulysses approached the bow shock. We report here the results of a systematic study on the statistical properties of these field depressions. We have found that there is a saturation in the level of low field at about 1.3 nT. The average duration of the depressions is about 40 s, corresponding to a spatial size of about 20 gyroradii of the plasma protons. The angle between the magnetic field vector and the minimum variance direction is almost perpendicular, the average of that angle for the 350 individual field depressions we have analyzed is 83°. Constraints on the theoretical models which these observations impose are discussed. Many characteristics of the field depressions suggest the importance of nonlinear effects. The longitudinal size of the weak field seems rather large, raising the question whether the particles have enough time to fill in that space during the development of the instability. This difficulty might be resolved if energetic particles are involv