In distributed development of modern systems, contracts play a vital role in ensuring interoperability of components and adherence to specifications. It is therefore often desirable to verify the satisfaction of an overall property represented as a contract, given the satisfaction of smaller properties also represented as contracts. When the verification result is negative, designers must face the issue of refining the subproperties and components. This is an instance of the classical synthesis problems: " can we construct a model that satisfies some given specification? " In this work, we propose two strategies enabling designers to synthesize or refine a set of contracts so that their composition satisfies a given contract. We develop a generic algebraic method and show how it can be applied in different contract models to support top-down component-based development of distributed systems.