A plane sound wave is incident upon an anisotropic rectangular plate set in an otherwise rigid baffle surrounded by a light compressible fluid. In the limit of small wavelengths, compared with plate dimensions, the transmitted sound power is estimated, averaged over a small frequency band and over all possible angles of incidence. Explicit results are presented for a special type of anisotropy, and they have different forms according as the operating frequency $\omega$ is above coincidence, below coincidence or within a range of frequencies ($\omega_2 < \omega < \omega_1$) that corresponds to coincidence. Transition formulae are given for frequencies near the boundaries of the three regimes. The results are extended to allow for more general plate equations.