This report presents results from an assessment of new methods for numerical prediction of active target signatures in hydroacoustics and electromagnetics. The methods are based on numerical solution of the governing integral equations with accelerated high-order techniques. Two methods of this type were considered, a partition of unity method (PUM) and an envelope method (ENM). Results are presented from computation of the bistatic hydroacoustic target strength of, respectively, an autonomous underwater vehicle and a mine, with ENM and with a conventional high-order method. The computational efficiency of ENM is in all test cases found to be significantly larger than that of the conventional method. The efficiency gain is decided by the rate of variation of the envelope of the acoustic pressure on the surface of the target, and is influenced by the frequency, the shape of the target and the direction of propagation of the incident field. The gain is particularly large at moderate accuracy demands (ca 1%-5%), and decreases when the accuracy demands are very large so that the spatial grid steps must be much smaller than the wavelength. The test cases could not be treated with the PUM method, since it was found to require complementary development that was too extensive for the time-frame available for this work.