A brief review of previous work and the present situation in the problem of formation of elliptical galaxies via dissipationless collapse are presented, as well as the results of a new set of numerical experiments. It is shown that collapses started from cold initial conditions are different from warmer collapses, due to the presence of a dynamical instability associated with radial orbits. This instability leads to triaxial final configurations, regardless of the initial amount of random kinetic energy, rotational kinetic energy, or shape of the initial conditions, as long as2T/W≲0.1, whereT is the total (rotational plus thermal) kinetic energy andW is the potential energy of the initial conditions. Warmer initial conditions preserve their initial shape, or become oblate if initially rotating. Cold initial conditions produce equilibrium systems with realistic density profiles, as opposed to collapses from warmer conditions that result in core-halo profiles, unlike the observed surface brightness profiles of elliptical galaxies. Although the same cold collapses that result in triaxial shapes produce realistic density profiles, it is shown that these two effects are not directly connected: cold collapses simulated with anN-body code that enforces spherical symmetry result in realistic density profiles too.