During the core bounce of a supernova collapse resonant active-to-active (νa→νa), as well as active-to-sterile (νa→νs) neutrino (ν) oscillations can take place. Besides, over this phase weak magnetism increases antineutrino [Formula: see text] mean free paths, and thus its luminosity. Because the oscillation feeds mass-energy into the target ν species, the large mass-squared difference between species (νa→νs) implies a huge amount of power to be given off as gravitational waves (L GWs ~1049 erg s -1), due to anisotropic but coherent ν flow over the oscillation length. This anisotropy in the ν-flux is driven by both the universal spin-rotation and the spin-magnetic coupling. The new spacetime strain estimated this way is still several orders of magnitude larger than those from ν diffusion (convection and cooling) or quadrupole moments of the neutron star matter. This new feature turns these bursts the more promising supernova gravitational-wave signal that may be detected by observatories as LIGO, VIRGO, etc., for distances far out to the VIRGO cluster of galaxies.