  We obtain the non-collinear ground states of a triangular-lattice
antiferromagnet with exchange interactions up to third nearest neighbors as a
function of the single-ion anisotropy $D$. At a critical value of $D$, the
collinear $\uudd $ phase transforms into a complex non-collinear phase with
odd-order harmonics of the fundamental ordering wavevector $\vQ $. The observed
elastic peaks at $2\pi \vx -\vQ $ in both Al- and Ga- doped CuFeO$_2$ are
explained by a "scalene" distortion of the triangular lattice produced by the
repulsion of neighboring oxygen atoms.
