Proteins with more than 1000 non-H atoms and without heavy-atom prosthetic groups are very difficult to solve by ab initio direct methods. T4 lysozyme is being used to explore these limits. The protein has 1309 non-H atoms, seven S atoms, no disulfide bonds and no heavy-atom prosthetic group. It is recalcitrant to structure determination by direct methods using X-ray diffraction data to 0.97 A. It is shown here that it is possible to obtain a truly ab initio structure determination of a variant of the protein that has an Rb+ (Z = 37) binding site. Using diffraction data to 1.06 A resolution, the direct-methods programs SIR2002 and ACORN independently solved the structure in about 20 h. The bound Rb+, which contributes about 1.7% of the total scattering, does not appear to distort the structure or to inhibit refinement (R factor 12.1%). The phases obtained via SIR2002 or ACORN are in good agreement with those from a reference structure obtained from conventional molecular-substitution and refinement procedures (average error in the figure-of-merit-weighted phases of less than 25 degrees). Thus, proteins with more than 1000 atoms that include halide-binding or other such sites may be amenable to structure determination by ab initio direct methods. The direct-methods approaches are also compared with structure determination via use of the anomalous scattering of the Rb+ ion. As shown by examples, high-resolution structures determined by direct methods can be useful in highlighting regions of strain in the protein, including short hydrogen bonds and non-planar peptide groups.