It is shown on the ground of a simple 6\times 6 neutrino mixing model that one of three conventional sterile (righthanded) neutrinos, if light enough, may be consistently used for explaining a  small LSND effect. Then, it is still considerably heavier than the three active (lefthanded) neutrinos, so that a kind of  soft seesaw mechanism can work. The usual condition that the Majorana lefthanded component of the overall 6\times 6 neutrino mass matrix ought to vanish,  implies the smallness of active-neutrino masses  versus sterile-neutrino masses, when three mixing angles between both sorts of neutrinos are small. In the presented model, the mass spectrum of active neutrinos comes out roughly degenerate, lying in the range (5-7.5)\times 10^-2 eV, if there is a  small LSND effect with the amplitude of the order 10^-3 and with the mass-squared splitting \sim 1 {eV}².

PACS numbers: 12.15.Ff, 14.60.Pq, 12.15.Hh