  We report on unusually very hard spectral states in three confirmed
neutron-star low-mass X-ray binaries (1RXS J180408.9-342058, EXO 1745-248, and
IGR J18245-2452) at a luminosity between ~ 10^{36-37} erg s^{-1}. When fitting
the Swift X-ray spectra (0.5 - 10 keV) in those states with an absorbed
power-law model, we found photon indices of \Gamma ~ 1, significantly lower
than the \Gamma = 1.5 - 2.0 typically seen when such systems are in their so
called hard state. For individual sources very hard spectra were already
previously identified but here we show for the first time that likely our
sources were in a distinct spectral state (i.e., different from the hard state)
when they exhibited such very hard spectra. It is unclear how such very hard
spectra can be formed; if the emission mechanism is similar to that operating
in their hard states (i.e., up-scattering of soft photons due to hot electrons)
then the electrons should have higher temperatures or a higher optical depth in
the very hard state compared to those observed in the hard state. By using our
obtained \Gamma as a tracer for the spectral evolution with luminosity, we have
compared our results with those obtained by Wijnands et al. (2015). We confirm
their general results in that also our sample of sources follow the same track
as the other neutron star systems, although we do not find that the accreting
millisecond pulsars are systematically harder than the non-pulsating systems.
