Conditions necessary to achieve deuterium-tritium fuel self-sufficiency in fusion reactors are derived through extensive modeling and calculations of the required and achievable tritium breeding ratios as functions of the many reactor parameters and candidate design concepts. It is found that the excess margin in the breeding potential is not sufficient to cover all present uncertainties. Thus, the goal of attaining fuel self-sufficiency significantly restricts the allowable parameter space and design concepts. For example, the required breeding ratio can be reduced by (a) attaining high tritium fractional burnup, >5%, in the plasma, (b) achieving very high reliability, >99%, and very short times, <1 day, to fix failures in the tritium processing system, and (c) ensuring that nonradioactive decay losses from all subsystems are extremely low, e.g., <0.1 % for the plasma exhaust processing system. The uncertainties due to nuclear data and calculational methods are found to be significant, but they are substantially smaller than those due to uncertainties in system definition.