This paper proposes a simple method for measuring the cost of explorative service composition. Based on this measurement two different solutions are proposed for Explorative Service Compositions in a stateless environment: the Eliminative Method and Two-Stage Explorative Parallel Composition. Each solution provides certain cost advantages that are dependent on the possibility of search failure of directory and access to services. Each solution is examined and compared according to their actual execution cost, cost during a failure and their potential for concurrency.