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The possibility for obtaining a hard neutron spectrum in small reactor cores has been considered. A harder spectrum than spectra in known fast sodium cooled and molten salt reactors has been obtained thanks to the selection of relatively small core dimensions and the use of metallic fuel and natural lead (natPb) coolant. The calculations for these compositions achieve an increased average neutron energy and a large fraction of hard neutrons in the spectrum (with energies greater than 0.8 MeV) caused by a minor inelastic interaction of neutrons with the fuel with no light chemical elements and with the coolant containing 52.3% of 208Pb, a low neutron-moderating isotope. An interest in creating reactors with a hard neutron spectrum is explained by the fact that such reactors can be practically used as special burners of minor actinides (MA), and as isotope production and research reactors with new consumer properties. With uranium oxide fuel (UO2) substituted by metallic uranium-plutonium fuel (U-Pu-Zr), the reactors under consideration have the average energy of neutrons and the fraction of hard neutrons increasing from 0.554 to 0.724 MeV and from 18 to 28% respectively. At the same time, the one-group fission cross-section of 241Am increases from 0.359 to 0.536 barn, while the probability of the 241Am fission increases from 22 to 39%. It is proposed that power-grade plutonium resulting from regeneration of irradiated fuel from fast sodium cooled power reactors be used as part of the fuel for future burner reactors. It contains unburnt plutonium isotopes and some 1% of MAs which transmutate into fission products in the process of being reburnt in a harder spectrum. This will make it possible to reduce the MA content in the burner reactor spent fuel and to facilitate so the long-term storage conditions for high-level nuclear waste in dedicated devices.