Using magnetic field data from the four Cluster spacecraft between February and May 2001, a detailed statistical analysis of interplanetary discontinuities is accomplished. In order to find the surface normals, we apply three different methods: (1) minimum variance analysis (MVA), (2) cross-product method, and (3) triangulation, the latter being the only one that needs information from all four spacecraft. Whereas the cross-product normals are always almost the same at the position of the four spacecraft, strong deviations between the MVA normals are observed. The cross-product normals also agree fairly well with the triangulation normals, which mostly point in a direction approximately perpendicular to the magnetic field. The scatter of the MVA normals around the triangulation normal can be reduced by triggering the parameters controlling the MVA accuracy, i.e., λ2/λ3L, the lower limit of the MVA eigenvalue ratio, and ωL, the lower limit of the spreading angle. Our analysis allows to compare the impact of these two parameters on the MVA normals. The error analysis shows that both parameters have strong impact on the MVA accuracy; however, λ2/λ3L is more important. In order to ensure reliable normal estimates, MVA should only be applied if ωL > 60¿. The MVA error analysis also enables us to provide a new criterion to distinguish rotational discontinuities (RDs) from tangential discontinuities. However, the triangulation results show that there are no clearly identified RDs in our data set. We will discuss implications for the theory of solar wind discontinuity generation processes. A practical consequence is that the cross-product method presumably yields better normal estimates than MVA when Bn is small. The colinerarity of the cross-product normals at the positions of the four spacecraft demonstrate that the discontinuities are one-dimensional structures on the Cluster separation scale.