Transactional Memory, one of the most viable alternatives to lock based concurrent systems, was explored by the researchers for practically implementing parallel processing. The goal was that threads will run parallel and improve system performance, but the effect of their execution will be linear. In STM, the non-blocking synchronization can be implemented by Wait-Freedom, Lock-Freedom or Obstruction-Freedom philosophy. Though Obstruction Free Transactional Memory (OFTM) provides the weakest progress guarantee, this paper concentrates upon OFTM because of its design flexibility and algorithmic simplifications. In this paper, the major challenges faced by two state of the art OFTMs viz. Dynamic Software Transactional Memory (DSTM) and Adaptive Software Transactional Memory (ASTM), have been addressed and an alternative arbitration strategy has been proposed that reduces the abort percentage both in case of Read-Write as well as Write-Write conflicts.