As a widely accepted performance measure in supply chain management practice, service level is often considered in supplier contracts under Vendor-Managed-Inventory (VMI) programs. Using a two-stage capacitated supply chain model consisting of one manufacturer and one supplier in a VMI environment, we demonstrate that supplier's service level is in general insufficient for the manufacturer to warrant the desired service level at the customer end. The method by which the supplier achieves its service level to the manufacturer also affects customer service level. Alternative measures should be explored which allow the manufacturer to control customer service regardless of how the supplier manages the inventory. We identify plausible supplier performance measures with this kind of property by developing bounds on the customer service level. We also derive an estimate of the customer service level in terms of the new measures.