The register file is one of the most critical datapath components limiting the number of threads that can be supported on a Simultaneous Multithreading (SMT) processor. To allow the use of smaller register files without degrading performance, techniques that maximize the efficiency of using registers through aggressive register allocation/deallocation can be considered. In this paper, we propose a novel technique to early deallocate physical registers allocated to threads that experience L2 cache misses. This is accomplished by speculatively committing the load-independent instructions and deallocating the registers corresponding to the previous mappings of their destinations, without waiting for the cache miss request to be serviced. The early deallocated registers are then made immediately available for allocation to instructions within the same thread as well as within other threads, thus improving the overall processor throughput. On the average across the simulated mixes of multiprogrammed SPEC 2000 workloads, our technique results in 33% improvement in throughput and 25% improvement in terms of harmonic mean of weighted IPCs over the baseline SMT with the state-of-the-art DCRA policy. This is achieved without creating checkpoints, maintaining per-register counters of pending consumers, performing tag re-broadcasts, register re-mappings and/or additional associative searches.