Computational grids allow the users to run their applications on remote high-performance servers available via Internet. Java is often used to develop portable grid applications, with programs being sequences (compositions) of remote method calls. We demonstrate an inherent inefficiency of the standard remote method invocation (RMI) mechanism of Java for implementing compositions of remote calls. We propose a new, optimised RMI mechanism, called future-based RMI, that substantially reduces the unnecessary communication overhead of method compositions in a grid environment. We present an analytical model for estimating the performance improvements achieved by our mechanism and report experimental results for two case studies on a grid testbed including a high-performance shared-memory server which is accessed from a client located 500 km away.