We used the N-body code of Hernquist & Ostriker to build a dozen cuspy (γ≃ 1) triaxial models of stellar systems through dissipationless collapses of initially spherical distributions of 106 particles. We chose four sets of initial conditions that resulted in models morphologically resembling E2, E3, E4 and E5 galaxies, respectively. Within each set, three different seed numbers were selected for the random number generator used to create the initial conditions, so that the three models of each set are statistically equivalent. We checked the stability of our models using the values of their central densities and of their moments of inertia, which turned out to be very constant indeed. The changes of those values were all less than 3 per cent over one Hubble time and, moreover, we show that the most likely cause of those changes are relaxation effects in the numerical code. We computed the six Lyapunov exponents of nearly 5000 orbits in each model in order to recognize regular, partially and fully chaotic orbits. All the models turned out to be highly chaotic, with less than 25 per cent of their orbits being regular. We conclude that it is quite possible to obtain cuspy triaxial stellar models that contain large fractions of chaotic orbits and are highly stable. The difficulty in building such models with the method of Schwarzschild should be attributed to the method itself and not to physical causes.