The deployment of high performance networks and the emergence of broadband wireless access technologies challenge the performance of standard TCP. Recent years have seen a few high performance and aggressive TCP variants being proposed. These TCP variants still suffer significant performance degradation from random/transient packet losses. In this paper, we introduce and evaluate a new method to improve high performance TCP in the presence of random packet losses. It is 'blind' in that our method does not attempt to differentiate between random and congestion-induced losses. Our method combines both TCP parallelisation and modification to the aggressiveness of studied AIMD algorithms. We show that our proposed method is no more aggressive than the studied TCP variants in the presence of congestion but more effectively utilises bandwidth in the presence of random packet losses.