We introduce a new traffic analysis attack: the Two-sided Statistical Disclosure Attack, that tries to uncover the receivers of messages sent through an anonymizing network supporting anonymous replies. We provide an abstract model of an anonymity system with users that reply to messages. Based on this model, we propose a linear approximation describing the likely receivers of sent messages. Using simulations, we evaluate the new attack given different traffic characteristics and we show that it is superior to previous attacks when replies are routed in the system.