This paper deals with ideal-MHD stability of equilibrium configurations modeling the plasma sheet of the Earth's magnetotail. The approach exploits the fact that in the absence of a cross-tail magnetic field component, the MHD stability problem for two-dimensional (2-D) equilibria under general 3-D perturbations can be reduced to analyzing stability with respect to ballooning modes alone. The correspondingly specialized MHD energy principle is numerically minimized for three different equilibrium models. In all cases the stability of symmetric modes was governed by the interchange criterion based on entropy. A constant background pressure is included, which, even if small, can have a significant stabilizing effect. An analytical approach provides a set of rather simple stability criteria, which are consistent with the numerical minimization results. A main conclusion is that configurations with realistic tailward pressure profiles are found stable. For all three models the entropy criterion implies that stability transitions of the symmetric mode cannot occur during the adiabatic evolution of ideal-MHD tail configurations.