Three crossings of the lobe plasma sheet boundaries encountered within Earth's distant magnetotail with the Geotail spacecraft are analyzed in terms of slow-mode shocks. Quantitative comparisons with theoretical predictions for a steady state, one-dimensional shock are made based upon measurements of the three-dimensional velocity distributions of protons and electrons and of the magnetic fields. The observed plasma moments and magnetic field upstream from the shock are successfully used to predict these parameters in the downstream region. Slow-mode Mach numbers in the upstream and downstream regions are also shown to be above and below unity, respectively, as required for the slow-mode shock transition. However, a consideration of the relative uncertainties for the upstream and downstream slow-mode Mach numbers allows convincing identifications for only two of the boundaries as slow-mode shocks. Low number densities of plasmas for the other boundary, ~0.1/cm3, are responsible for the large relative uncertainties for the Mach numbers. This analysis of slow-mode shocks, together with a comprehensive accounting of statistical uncertainties and variances, allows us to provide firm evidence for the existence of slow-mode shocks in Earth's distant magnetotail. ¿ American Geophysical Union 1996