Possibilities are discussed for determining the top-quark mass m(t) fr
om observations on the decay processes for top-antitop pairs produced
in antiproton-proton collisions at Tevatron energies, assuming that th
e t --> bW+ decay channel is dominant and much faster than hadronizati
on. The final states ttBAR --> bbmuBAR+/-e-/+ provide the most strikin
g signal, with little background, but they are rare (almost-equal-to 2
/81). If all three candidate events prove to be from ttBAR, an estimat
e follows for P(m(t)/rate), the probability distribution for m(t). The
one reported configuration allows an independent estimate for P (m(t)
\mu+/-e-/+ 2 jets). These two distributions are compatible and can be
combined to give an m(t) estimate of Decay events ''1 energetic lepton
(l) + 4 jets'' should appear 12 times as often as ''mu+/-e-/+ 2 jets''
events and can be analyzed to give estimates for P(m(t)/l 4 jets); th
is is illustrated for a fictitious event. There may be background from
nontop events but suitable cuts on the data and our analysis procedur
e together reduce this to a low level. The rate observed for these eve
nts does not appear to be as large as the factor 12. Identification of
either or both of the (b, bBAR) jets would be a great step forward, s
eparating out the ''mu+/-e-/+bbBAR'' and ''lbbBAR 2 jets'' events of i
mportance with little background. We advocate an energetic approach to
the analysis of individual events [whether 2, 1 or no (b or bBAR) jet
s identified] on an event-by-event basis, with the hope of finding a s
ubgroup of events with a common mass estimate.