We use the two most recent empirical magnetosphere models of Tsyganenko [1987; 1989> to find the energy dependent boundary of isotropic precipitation due to the nonadiabatic particle motion in the nightside current sheet. Model predictions are compared with the earlier published satellite observations of this boundary at low altitudes. A dramatic difference has been found between the predicted position of the isotropy boundary based on T87 and T89 model. The most recent magnetosphere model of Tsyganenko featuring the warped current sheet with thickness dependent both on XGSM and YGSM predicts that the isotropy boundary is situated at much lower latitudes than inferred from the previous models. This is in agreement with observations. However, even this model with very stretched tail magnetic field lines has difficulties in explaining the frequently observed very steep profile of critical rigidity vs L. ¿American Geophysical Union 1991