A key goal of the Services Oriented Architecture is the composition of independently written and managed services. However, managing access to these services has proven to be a problem. A particularly difficult case involves a service that invokes another service to satisfy an initial request. In a number of cases, implementations are able to achieve either the desired functionality or the required security, but not both at the same time. We say that this service composition suffers from the transitive access problem. We show that the problem arises from a poor choice of access control mechanism, one that uses subject authentication to make access decisions, and that the problem does not occur if we use delegatable authorizations.