In the Tokamak Fusion Test Reactor (TFTR) [Plasma Phys. Controlled Fusion 26, 11 (1984)], the highest neutron source strength Sn and D–D fusion power gain QDD are realized in the neutral-beam-fueled and heated ‘‘supershot’’ regime that occurs after extensive wall conditioning to minimize recycling. For the best supershots, Sn increases approximately as P1.8b. The highest-Q shots are characterized by high Te (up to 12 keV), Ti (up to 34 keV), and stored energy (up to 4.7 MJ), highly peaked density profiles, broad Te profiles, and lower Zeff. Replacement of critical areas of the graphite limiter tiles with carbon-fiber composite tiles and improved alignment with the plasma have mitigated the ‘‘carbon bloom.’’ Wall conditioning by lithium pellet injection prior to the beam pulse reduces carbon influx and particle recycling. Empirically, QDD increases with decreasing pre-injection carbon radiation, and increases strongly with density peakedness [ne(0)/〈ne〉] during the beam pulse. To date, the best fusion results are Sn=5×1016 n/sec, QDD=1.85×10−3, and neutron yield=4.0×1016 n/pulse, obtained at Ip=1.6–1.9 MA and beam energy Eb=95–103 keV, with nearly balanced co- and counter-injected beam power. Computer simulations of supershot plasmas show that typically 50%–60% of Sn arises from beam–target reactions, with the remainder divided between beam–beam and thermonuclear reactions, the thermonuclear fraction increasing with Pb. The simulations predict that QDT=0.3–0.4 would be obtained for the best present plasma conditions, if half the deuterium neutral beams were to be replaced by tritium beams. Somewhat higher values are calculated if D beams are injected into a predominantly tritium target plasma. The projected central beta of fusion alphas is 0.4%–0.6%, a level sufficient for the study of alpha-induced collective effects.