The properties of small-amplitude waves propagating in a homogeneous anisotropic plasma are investigated using an MHD double-polytropic model that incorporates the CGL double-adiabatic model in one extreme and the isothermal model in the other. It is found that the properties of fast and intermediate mode waves remain qualitatively the same as in ordinary MHD but that, in certain parameter regimes, three inversions occur for slow-mode waves: (1) their phase speed exceeds that of intermediate waves; (2) they behave like fast-mode waves in that, across them, the plasma density and magnetic field increase or decrease together; (3) rarefaction waves rather than compression waves steepen. ¿ American Geophysical Union 1993