A recent analysis of supernova (SN) 2002bj revealed that it was an apparently unique type Ib SN. It showed a high peak luminosity, with absolute magnitude M_R -18.5, but an extremely fast-evolving light curve. It had a rise time of <7 days followed by a decline of 0.25 mag per day in B-band, and showed evidence for very low mass of ejecta (<0.15 M_Sun). Here we discuss two additional historical events, SN 1885A and SN 1939B, showing similarly fast light curves and low ejected masses. We discuss

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... the low mass of ejecta inferred from our analysis of the SN 1885A remnant in M31, and present for the first time the spectrum of SN 1939B. The old environments of both SN 1885A (in the bulge of M31) and SN 1939B (in an elliptical galaxy with no traces of star formation activity), strongly support old white dwarf progenitors for these SNe. We find no clear evidence for helium in the spectrum of SN 1939B, as might be expected from a helium-shell detonation on a white dwarf, suggested to be the origin of SN 2002bj. Finally, the discovery of all the observed fast-evolving SNe in nearby galaxies suggests that the rate of these peculiar SNe is at least 1-2 % of all SNe.