The neutrino masses and mixings indicated by current neutrino oscillation experiments suggest that the neutrino mass matrix possesses an approximate μ–τ exchange symmetry. In this study, we explore the neutrino parameter space and show that if a small μ–τ symmetry breaking is considered, the Majorana CP phases must be unequal and non-zero independently of the neutrino mass scale. Moreover, a small μ–τ symmetry breaking favors quasi-degenerate masses. We also show that Majorana phases are strongly correlated with the Dirac CP violating phase. Within this framework, we obtain robust predictions for the values of the Majorana phases when the experimental indications for the Dirac CP phase are used.