Permitting procedures for hazardous waste incinerators usually require a test burn in which the incinerator is shown to achieve at least 99.99% destruction of the principal hazardous components. Hazardous waste incinerators are designed to achieve this goal with a substantial safety margin. Unfortunately, however, they sometimes fail to achieve the required degree of destruction of the material, especially when the hazardous materials are present in low initial concentrations. Theoretical arguments are advanced which show that the conventional tests of incinerability involve a fallacy and can overestimate the extent to which a hazardous material will be destroyed. These arguments are supported by computer modeling and directly confirmed by laboratory measurements. A novel method for improving incinerator effectiveness is proposed. Computer modeling shows that this method can be highly effective and experiments with a number of difficult to incinerate, hazardous chemicals show that improvements in incinerator effectiveness of 1,000 or more can be achieved. Commercialization of this technology would allow incinerators to destroy toxic organic materials with reduced emissions of those materials to the atmosphere. While this is of critical importance to incinerators used to destroy dioxins, PCBs, nerve gases, and other extremely toxic materials, the costs of this improvement are thought to be modest, and the scheme is expected to have broad applicability.