The plane-wave pseudopotential method is used to calculate structural properties for wurtzite and zinc-blende AlN and InN using large plane-wave basis sets and treating the indium 4[ital d] electrons as valence. These calculations, together with corresponding ones for GaN [A. F. Wright and J. S. Nelson, Phys. Rev. B 50, 2159 (1994)], yield a consistent set of well-converged structural properties for AlN, GaN, and InN. In particular, the measured lattice mismatch among these compounds---essential for an accurate description of alloy properties---is well reproduced.