Possibilities are discussed for determining the top-quark mass m(t) from observations on the decay processes for top-antitop pairs produced in antiproton-proton collisions at Tevatron energies, assuming that the t --> bW+ decay channel is dominant and much faster than hadronization. The final states ttBAR --> bbmuBAR+/-e-/+ provide the most striking signal, with little background, but they are rare (almost-equal-to 2/81). If all three candidate events prove to be from ttBAR, an estimate 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); this is illustrated for a fictitious event. There may be background from nontop events but suitable cuts on the data and our analysis procedure together reduce this to a low level. The rate observed for these events 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, separating out the ''mu+/-e-/+bbBAR'' and ''lbbBAR 2 jets'' events of importance with little background. We advocate an energetic approach to the analysis of individual events [whether 2, 1 or no (b or bBAR) jets identified] on an event-by-event basis, with the hope of finding a subgroup of events with a common mass estimate.