  This paper proposes a new approach for the selection of low-energy neutrino
bursts, such as the ones detected after a supernova. It exploits the temporal
structure of the expected signal with respect to the more diffuse background by
defining a "Real-time Test Statistic" (RTS) that would allow identifying very
weak signals, hard to select using standard clustering methods. For a given
background rate, the new method (RTS$^2$: RTS for Supernovae) increases signal
efficiency while keeping the same false alarm rate for Poisson-distributed
background. By adding a spatial penalty term to the definition of RTS, one can
also reject spatially-correlated backgrounds such as the ones due to spallation
events. Furthermore, the method is easy to implement in a real-time monitoring
system as RTS can be computed recursively for successive events, and it can be
easily adapted for detectors of all scales that may want to send prompt alerts
e.g. through SNEWS 2.0 network.
