We study the Complex Absorbing Potential (CAP) Method in computing quantum resonances of width -Im z(h) ≤ c(h) = O(h^N), N >> 1. We show that up to an error, M >> 1, resonances are perturbed eigenvalues of the CAP Hamiltonian P(h) - i W, and vice versa, where W is the CAP with non-negative real part supported outside the trapping region. In some cases, the error terms are exponentially small.