Abstract While the combined SNO-SuperKamiokande solar results require only the three known active neutrinos, adding the atmospheric neutrino and LSND input would require a fourth, sterile neutrino, ν s . The LSND results, which alone force appreciable hot dark matter, are unlikely to be accommodated by a 3+1 neutrino scheme, so it is important to know if the 2+2 scheme survives. For the latter, if the fraction of sterile neutrinos is denoted by η S for the solar flux and η A for the atmospheric flux, we show that 1) for ν μ purely in the atmospheric neutrino pair and ν e purely in the solar pair, η S + η A ≥ 1 for any arbitrary number of neutrinos, and 2) there is considerable deviation from that sum rule if a small fraction of the ν μ and ν e mix into the opposite pairs of mass states. Thus 2+2, sterile neutrinos, and hot dark matter can survive.