Fusion power density Pf is a critical parameter for certain fusion reactor applications such as fissile breeding. This paper considers the optimal plasma conditions for maximizing Pf in a beam-driven D-T tokamak reactor. Given Te=Ti and fixed total plasma pressure, there is an optimal neτE for maximizing Pf, i.e. neτE = 4 × 1012 to 2 × 1013 cm−3 · s for Te = 3 – 15 keV and 200-keV D beams. The corresponding = (beam pressure/bulk-plasma pressure) is 0.96 to 0.70. Pfmax increases as Te is reduced and can be an order of magnitude larger than the maximum Pf of a thermal reactor of the same beta, at any temperature. A lower practical limit to Te may be set by requiring a minimum beam power multiplication Qb. For the purpose of fissile breeding, the minimum Qb ∼ 0.8, requiring Te⪆ 4 keV if Z = 1.The optimal operating conditions for obtaining Pfmax in a beam-driven reactor are considerably different from those for enhancing Qb. Maximizing Pf requires restricting both Te and neτE, maintaining a bulk plasma markedly enriched in tritium, and spoiling confinement of fusion alphas. Provided that beam penetration is satisfactory, considerable impurity content can be tolerated without seriously degrading Pfmax.