Computational protein design relies on a number of approximations to efficiently search the huge sequence space available to proteins. The fixed backbone and rotamer approximations in particular are important for formulating protein design as a discrete combinatorial optimization problem. However, the resulting coarse-grained sampling of possible side-chain terminal positions is problematic for the design of protein function, which depends on precise positioning of side-chain atoms. Although backbone flexibility can greatly increase the conformation freedom of side-chain functional groups, it is not obvious which backbone movements will generate the critical constellation of atoms responsible for protein function. Here, we report an automated method for identifying protein backbone movements that can give rise to any specified set of desired side-chain atomic placements and interactions, using protein-DNA interfaces as a model system. We use a library of previously observed protein-DNA interactions (motifs) and a rotamer-based description of side-chain conformation freedom to identify placements for the protein backbone that can give rise to a favorable side-chain interaction with DNA. We describe a tree-search algorithm for identifying those combinations of interactions from the library that can be realized with minimal perturbation of the protein backbone. We compare the efficiency of this method with the alternative approach of building and screening alternate backbone conformations.