In this paper, we study a finitely repeated Prisoner's Dilemma in which players are asymmetric in both their temptation to deviate from cooperation and their level of patience, as captured by their discount factors. We investigate whether a profile of limited retaliation strategies constitutes a perfect \(\varepsilon\)-equilibrium. These strategies impose a mild punishment on the first player to deviate and allow cooperation to resume after a finite retaliation period. Any subsequent deviation is punished until the end of the game. A key feature of these strategies is that, when it exists, the duration of the retaliation period need not be unique. We characterize both ex ante and contemporaneous perfect \(\varepsilon\)-equilibria and show how the duration of the retaliation period depends on asymmetries in the game's parameters.