We studied the aggressive behavior of territorial male fallow deer (Dama dama) at two leks. Daily number of escalated fights was not correlated with number of matings. A dominance index including all agonistic interactions was weakly correlated with copulatory success; the correlation was stronger when each half of the rut was considered separately. Dominance likely changed over the rut due to fatigue. We ranked lek territories by the number of copulations seen in each. Males that won fights were likely to take over the loser's territory only if it ranked higher than the one they held. Winners were more likely to fight with a third male after defeating an opponent that held a higher-ranking territory than one from a lower-ranking territory. Exposure to attacks by third-party males may be a major cost of fighting. Males appear aware of the relative value of different lek territories, but the frequency of aggression was not scaled to potential fitness benefits, possibly because males seldom fought with opponents they were unlikely to beat. The outcome of interactions on the lek may not always reflect the relative dominance rank of the contestants. Females are unlikely to use the outcome of fights as a direct criterion for mate selection.