Analytical expressions for the growth rates of unstable low-frequency 'fast' modes are derived here in the low-frequency, low-&bgr;, limit for a plasma obeying classical linear transport theory. The results indicate that at the onset of instability (~10Rs from the sun) the first growing mode in the solar wind has a frequency of ~0.1 times the proton gyrofrequency and propagates at an appreciable angle to the background magnetic field. Substantial inhomogeneity is required for the growth to overcome competing processes. These modes may have consequences for thermal conduction, proton and helium heating, the observable wave spectrum, and other facets of solar wind theory, though considerable additional theory will be required.