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Software Transactional Memories (STMs) are emerging as a potentially disruptive programming model. In this paper we are address the issue of how to enhance dependability of STM systems via replication. In particular we present AGGRO, an innovative Optimistic Atomic Broadcast-based (OAB) active replication protocol that aims at maximizing the overlap between communication and processing through a novel AGGRessively Optimistic concurrency control scheme. The key idea underlying AGGRO is to propagate dependencies across uncommitted transactions in a controlled manner, namely according to a serialization order compliant with the optimistic message delivery order provided by the OAB service. Another relevant distinguishing feature of AGGRO is of not requiring a-priori knowledge about read/write sets of transactions, but rather to detect and handle conflicts dynamically, i.e. as soon (and only if) they materialize. Based on a detailed simulation study we show the striking performance gains achievable by AGGRO (up to 6x increase of the maximum sustainable throughput, and 75% response time reduction) compared to literature approaches for active replication of transactional systems.