Modularity in product design and flexible supply chains is increasingly common in buyer–supplier relationships. Although the benefits of supply chain flexibility and component modularity for end-product manufacturers are accepted, little is known about their impact on suppliers. We advance the literature on modularity by exploring how three aspects of a supplier’s relationships with its customers affect the supplier’s survival: duration of buyer–supplier relationships, autonomy from customers, and links to prominent buyers. We compared the effects of these aspects of buyer–supplier relationships for low- and high-modularity components. Using data on U.S. carburetor and clutch manufacturers from 1918 to 1942, we found that suppliers of high-modularity components benefited more from autonomy provided by potential customers, whereas suppliers of low-modularity components benefited more from ties to higher status customers. Both benefited from autonomy generated by existing customers. Thus, relationships that require trust and extensive sets of inter-firm routines, as do those for low-modularity components, led to both greater relationship benefits and greater constraints.