The optimization of ab initio molecular geometries is discussed. Based on comparisons of 30 minimizations and 15 saddle-point optimizations, the most efficient combination of coordinate system, approximate and exact Hessians, and step control is determined. Use of a proposed set of extra-redundant internal coordinates is shown to reduce the number of geometry steps significantly relative to the use of redundant coordinates. Various update schemes are tested for minimum and saddle-point optimizations, including combination formulas. The complete expressions for the first and second derivatives of the Wilson B matrix are presented, thereby avoiding the need to calculate this by finite-difference methods. The presented scheme appears to be the most efficient, robust and generally applicable scheme to date.