Most giant exoplanets discovered by radial velocity surveys have much higher eccentricities than those in the solar system . The planet–planet scattering mechanism has been shown to match the broad eccentricity distribution , but the highest-eccentricity planets are often attributed to Kozai-Lidov oscillations induced by a stellar companion . Here we investigate whether the highly eccentric exoplanet population can be produced entirely by scattering . We ran 500 N-body simulations of closely packed giant-planet systems that became unstable under their own mutual perturbations . We find that the surviving bound planets can have eccentricities up to e > 0.99 , with a maximum of 0.999017 in our simulations . This suggests that there is no maximum eccentricity that can be produced by planet–planet scattering . Importantly , we find that extreme eccentricities are not extremely rare ; the eccentricity distribution for all giant exoplanets with e > 0.3 is consistent with all planets concerned being generated by scattering . Our results show that the discovery of planets with extremely high eccentricities does not necessarily signal the action of the Kozai-Lidov mechanism .