In monogamous mammals it is often unclear why males do not defend larger territories to attract more than one female. I investigated the territoriality of the monogamous Kirk's dikdik, Madoqua kirki, a dwarf antelope, in which food resources increase with territory size and some males defend enough resources for more than one female. Yet, all males are paired monogamously. When males were removed from small territories, their female partners spent more time outside of their territories than females in large ones. When females were removed, their male partners almost never left. Pairs in small territories spent more time together than pairs in large ones. Paired males left mostly together with their females, apparently not on their own initiative. Presumably because females in small territories left more often, their males spent more time outside in the female's company than males in large territories. I argue that males in smaller territories can keep better track of their females and that they can effectively reduce their females' time outside. Male intrusion pressure was unrelated to territory size, but it increased in the presence of unguarded females. If large territories decrease the ability to mate guard, and if unguarded females attract competing males, then defending large territories may be uneconomical, even it they could attract more than one female. On the other hand, territories must be large enough to satisfy the requirements of a single female.