The first short Chandra and XMM-Newton observations of the young and energetic pulsar J1357-6429 provided strong 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 above 50% and a thermal component dominating at lower photon energies (below 2 keV). The elongated nebula is very compact in size and may 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+/-0.1 K temperature, covered with a magnetized hydrogen atmosphere. At higher energies the pulsars emission is of a nonthermal (magnetospheric) origin, with a power-law spectrum of a photon index of 1.1-1.3. This makes the X-ray properties of PSR J1357-6429 very similar to those of the youngest pulsars J1119-6127 and Vela with a detected thermal radiation.
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