The backscattering of an electromagnetic missile from a perfectly conducting curved obstacle is investigated. The obstacle is assumed to have zero curvature just at the point of reflection of the incident pulse. The asymptotic dependence of the backscattered energy is sought, as the distance separating the obstacle from the source of the incident pulse tends to infinity. The backscattered energy is found to depend on the rate at which the energy spectral density of the current pulse at the source decays with increasing frequency, as well as on the degree of flatness of the obstacle at the point of reflection. ©1996 American Institute of Physics.