In this paper we examine the approach of enabling parallel processing of general applications on top of Grids by adapting and extending methods that have been used successfully for tightly coupled systems. Our approach is based on the fundamental design of the Software Distributed Shared Memory (SDSM) model which we use in order to achieve the performance objectives of our environment. In this work we propose a new dynamically Reduced Message Protocol (RMP) for DSM systems, which adopts the scope-consistency model[8]. First, we outline our basic RMP protocol and then we propose two enhancements: the RMP-MH (Multiple Home)and the RMP-LM (Lock Migration). Our experimentation with RMP resulted in significant improvements by reducing the total messages and the overall number of page faults. In order to demonstrate the efficiency and the effectiveness of the RMP protocol we used SPLASH as well as synthetic application benchmarks, to highlight the protocols advantages, demonstrating a reduction in the total execution time of up to 30% for SPLASH applications and up to 61% for the synthetic application benchmarks.