Photometric and spectroscopic data on the Type Ib SN 1984L and the pro
bable Type lb SN 1985F near maximum light and at late times appear to
lead to contradictory conclusions. At early times a low mass and/or a
high explosion energy is indicated, while at late times a high mass an
d/or a low explosion is indicated. Several possibilities for resolving
the discrepancy are considered. The ejection of approximately 50 M. o
f helium with a kinetic energy of approximately 2 x 10(52) ergs, littl
e intermediate mass elements, and approximately 0.2 M. of Ni-56, might
satisfy the observational constraints. The astrophysical site of such
an explosion is elusive although a massive star that leaves behind a
massive black hole is a possibility. Some problems that make this scen
ario unappealing are discussed.