Two-dimensional realizations of self-consistent models for the "perfect elliptic disks" were tested for global stability by gravitational N-body integration. The family of perfect elliptic disk potentials have two isolating integrals; time-independent distribution functions f(E, I₂), which self-consistently reproduce the density distribution, can be found numerically, using a modified marching scheme to compute the relative contributions of each member in a library of orbits. The possible solutions are not unique; for a given ellipticity, the models can have a range of angular momenta. Here results are presented for cases with minimal angular momentum, hence maximal random motion. As in previous work, N-body realizations were constructed using a modified quiet start technique to place particles on these orbits uniformly in action-angle space, making the initial conditions as smooth as possible. The most elliptical models initially showed bending instabilities; by the end of the run they had become slightly rounder. The most nearly axisymmetric models tended to become more elongated, reminiscent of the radial orbit instability in spherical systems. Between these extremes, there is a range of axial ratios 0.305 b/a 0.570 for which the minimum streaming models appear to be stable.