The structures of protein complexes allow us to understand and modulate the biological functions of the proteins. Integrative docking is a computational method to obtain the structures of a protein complex, given the atomic structures of the constituent proteins along with other experimental data on the complex, such as chemical cross-links or SAXS profiles. Here, we develop a new discrete geometry-based method, wall-EASAL, for integrative rigid docking of protein pairs given the structures of the constituent proteins and chemical cross-links. The method is an adaptation of efficient atlasing and search of assembly landscapes (EASAL), a state-of-the-art discrete geometry method for efficient and exhaustive sampling of macromolecular configurations under pairwise intermolecular distance constraints. We provide a mathematical proof that the method finds a structure satisfying the cross-link constraints under a natural condition satisfied by energy landscapes. We compare wall-EASAL with integrative modeling platform (IMP), a commonly used integrative modeling method, on a benchmark, varying the numbers, types, and sources of input cross-links, and sources of monomer structures. The wall-EASAL method performs similarly to IMP in terms of the average satisfaction of the configurations to the input cross-links and the average similarity of the configurations to their corresponding native structures. But wall-EASAL is more efficient than IMP and more robust against false positive cross-links in the context of binary integrative rigid docking. Although the current study uses cross-links, the method is general and any source of distance constraints can be used for integrative docking with wall-EASAL. However, the current implementation only supports binary rigid protein docking, i.e., assumes that the monomer structures are known and remain rigid. Additionally, the current implementation is deterministic, i.e., it does not account for some uncertainties in the cross-linking data, such as noise in the cross-link distances. Neither of these appears to be a theoretical or algorithmic limitation of the EASAL methodology. Structures from wall-EASAL can be incorporated in methods for modeling large macromolecular assemblies, for example by suggesting rigid bodies or restraints for use in these methods. This will facilitate the characterization of assemblies and cellular neighborhoods at increased efficiency, accuracy, and precision. The wall-EASAL method is available at https://bitbucket.org/geoplexity/easal-dev/src/Crosslink and the benchmark is available at https://github.com/isblab/Integrative_docking_benchmark.