The CP-angles alpha, beta and gamma can be extracted from CP-violating asymmetries in the B system, but only up to discrete ambiguities. These discrete ambiguities make it difficult to determine with certainty whether or not new physics is present. I show that, if the condition alpha + beta + gamma = pi is imposed, there remains a twofold ambiguity in the CP-angle set (alpha,beta,gamma), and I discuss ways to cleanly resolve this final discrete ambiguity.