  We discuss the electron antineutrino fluence derived from the events detected
by Kamiokande-II, IMB and Baksan on February 23, 1987. The data are analysed
adopting a new simple and accurate formula for the signal, improving on the
previous modeling of the detectors response, considering the possibility of
background events. We perform several alternative analyses to quantify the
relevance of various descriptions, approximations and biases. In particular, we
study the effect of: omitting Baksan data or neglecting the background, using
simplified formulae for the signal, modifying the fluence to account for
oscillations and pinching, including the measured times and angles of the
events, using other descriptions of detector response, etc. We show that most
of these effects are small or negligible and argue, by comparing the allowed
regions for astrophysical parameters, that the results are stable. We comment
on the accordance with theoretical results and on open questions.
