We investigate whether dissipationless collapse starting from very cold, non-rotating initial conditions can produce objects resembling real elliptical galaxies. We also study the effect of various initial geometries on the shape of the final object. Collapses that are initially very cold (2T/W < 0.1) are different from warmer collapses, due to the presence of a dynamical instability associated with clumping of nearly-radial orbits (Polyachenko 1981). This instability can produce very elongated bars (1.6 to 2.1 axis ratio) from spherical initial conditions. the instability is also present in models evolved from oblate and triaxial initial conditions. Warm collapses tend to preserve their initial shapes. Cold initial conditions produce objects whose surface density profiles are well fit by a de-Vaucouleurs law; warm collapses, on the other hand, produce a core-halo profile. A large collapse factor seems necessary to produce objects resembling real galaxies; the same collapse factor guarantees the presence of the radial orbit instability. It thus appears that initial flattening is not crucial for producing prolate or nearly prolate galaxies. Oblate galaxies, on the contrary, seem very difficult to form, unless extremely flattened initial conditions are invoked. Preliminary experiments suggest that these results are not changed by realistic amounts of angular momentum.