The first short Chandra and XMM -Newton observations of the young and energetic pulsar J1357–6429 provided indications of a tail-like pulsar-wind nebula associated with this object , as well as pulsations of its X-ray flux with a pulsed fraction p _ { f } \gtrsim 50 % and a thermal component dominating at energies E \lesssim 2 keV . The elongated nebula is very compact in size and might be interpreted as evidence for a pulsar jet . The thermal radiation is most plausibly emitted from the entire neutron star surface of a 10 km radius and a 1.0 \pm 0.1 MK temperature , covered with a hydrogen atmosphere . At higher energies the pulsar ’ s emission is of a nonthermal origin , with a power-law spectrum of a photon index \Gamma = 1.1 \pm 0.2 . This makes the properties of PSR J1357–6429 very similar to those of the young pulsars J1119–6127 and Vela with detected thermal radiation .