It is well known that a pure-strategy Nash equilibrium does not exist for a two-player rentseeking contest when the contest success function parameter α is greater than two. We analyze the contest using the concept of an equilibrium in secure strategies, which is a generalization of the Nash equilibrium. It is defined by two conditions: no one can get profit from worsening the situation of other players and no one can get profit without creating a threat to lose more than he gains. We show that such an equilibrium always exists. Moreover, for α > 2 it is unique up to a permutation, and has a lower rent dissipation than in a mixed-startegy Nash equilibrium.