In this paper the approximate Lambda-Operator (ALO) developed by Olson, Auer and Buchler (OAB, 1986) is inspected from a more mathematical standpoint and compared to presently most commonly applied ALOs. For simple model calculations,it is shown that OAB's operator which contains no arbitrary parameter always works close to the optimum convergence rate. This operator is then applied for the first time to realistic NLTE calculations for hydrostatic atmospheres of hot stars, where it turns out that OAB's operator always leads to the fastest convergence rate and that this can be attained even for the most difficult case of nearly pure resonance scattering where other ALOs fail.