The influence of scattering and diffraction on the performance of sound intensity probes has been examined using a boundary element model of an axisymmetric two-microphone probe with the microphones in the usual face-to-face arrangement. On the basis of calculations for a variety of sound field conditions and probe geometries it is concluded that the optimum length of the spacer between the microphones is about one microphone diameter; with this geometry the effect of diffraction and the finite difference error almost counterbalance each other up to about an octave above the frequency limit determined by the finite difference approximation. This seems to be valid under virtually any sound field condition that could be of practical importance in sound power determination. The upper frequency limit corresponds to about 10 kHz for an intensity probe with12-in.microphones, which means that it should be possible to cover most of the audible frequency range, say, from 50 Hz to 10 kHz, with a single probe configuration. The numerical results have been confirmed by a series of experiments.