  We present a modification of the recently proposed Sorkin-Johnston states for
scalar free quantum fields on a class of globally hyperbolic spacetimes
possessing compact Cauchy hypersurfaces. The modification relies on a smooth
cutoff of the commutator function and leads always to Hadamard states, in
contrast to the original Sorkin-Johnston states. The modified Sorkin-Johnston
states are, however, due to the smoothing no longer uniquely associated to the
spacetime.
