The statistical disclosure attack (SDA) is an effective method for compromising the anonymity of users in a mix based system. Cover traffic, in the form of fake or dummy messages sent by other users of the mix, is an effective defense to make the task of the attacker difficult. Our aim is to examine the effect that background cover - the cover traffic sent by other users - has on the effectiveness of statistical disclosure attacks. Since the original SDA does not explicitly account for background traffic volumes, we developed an extension to the SDA called SDA-2H that uses this information to improve upon the SDA. Based on this attack, we are able to quantify the importance of background cover traffic, which we show in simulation to be effective in many scenarios.