When the emperor John I Tzimiskes campaigned against the Kievan Rus in 971, Anemas joined the expedition and went on to fight in a number of engagements during the Siege of Dorostolon. According to Leo the Deacon, during a sally of the besieged Rus, Anemas personally engaged and killed their second-in-command, Ikmor. On the next day (Leo gives it as Friday the 24th of July, but the 24th was a Monday) the Rus launched a determined all-out attack around sunset, hoping to break through. Anemas charged the Rus leader, Sviatoslav, and struck him on the neck, throwing him off his horse; his armour however saved Sviatoslav, and the Rus quickly came to his aid and attacked Anemas. The latter was able to kill several, but in the end was killed himself. The Rus then charged with renewed confidence, but were beaten back with heavy casualties, forcing Sviatoslav to capitulate and sign a treaty with Tzimiskes.