Suppliers of capital goods increasingly offer performance-based service contracts with customer-specific service levels. We use selective emergency shipments of spare parts to differentiate logistic performance: We apply emergency shipments in out-of-stock situations for combinations of parts and customer classes that yield service levels close to the class-specific targets. We develop two heuristics to solve this problem. An extensive numerical experiment reveals average cost savings of 4.4% compared to the one-size-fits-all approach that is often used in practice. It is best to combine our policy with critical levels, which yields an average cost saving of 13.9%.