We investigate, in a process algebraic setting, a new notion of compliance that we call strong service compliance: composed services are strong compliant if their composition is both deadlock and livelock free (this is the traditional notion of compliance) and whenever a message can be sent to invoke a service, this service is ensured to be ready to serve the invocation. We define also a new notion of refinement, called strong subcontract pre-order, suitable for strong compliance: given a composition of strong compliant services each one executing according to some specific contracts, we can replace the services with other services executing corresponding strong subcontracts preserving strong compliance. Finally, we present a characterization of the strong subcontract pre-order resorting to the theory of (should) testing pre-order.