The T, B and P axes of earthquake moment tensors (MT) are often used to evaluate regional stress directions and other tectonic parameters; we here undertake three comparisons to assess the uncertainty in the orientations of these axes. These are (1) a direct comparison of common MT in the Harvard, U.S. Geological Survey, or Earthquake Research Institute (ERI) catalogs; (2) a comparison of MT slip vectors and plate motion vectors in several tectonically straightforward regions; and (3) an analysis of the axial variability in the Harvard and ERI catalogs implied by the reported uncertainties in individual MT components. All three comparisons indicate that there is considerable variability within the catalog concerning the axial orientation of MT, but all suggest that axis orientations of the majority of Harvard MT have uncertainties of 15¿ or less. For compensated linear vector dipole (CLVD) components among the three catalogs, the correlation is very low. For the Harvard catalog, three statistics are especially useful for selecting better constrained MT; these are (1) the relative error Erel, which is the ratio of the scalar moments of the reported error tensor and of the MT itself; (2) fCLVD, a measure of the strength of the CLVD component; and (3) nfree, the number of MT elements not fixed at zero in the inversion. For selecting better constrained MT, the appropriate statistical cutoffs chosen depend on the problem of interest, the data available, and personal preference. However, for analysis of shallow earthquakes we have used Erel≤0.15, fCLVD≤0.20, and nfree=6. While this eliminates 53% of the catalog, our calculations suggest that nearly all the remaining events have T, B, and P axes with azimuth and inclination angle uncertainties of 5¿--10¿ or less. ¿ 1999 American Geophysical Union