The unrestricted Hartree-Fock UHF method is often advocated for "singlet" diradicals. Here, we examine the behavior of unrestricted Moller-Plesset (UMP) for the case where the spin along the "up" direction, M, is zero when the "triplet" is the true ground state. In this case, the UMP result should try to approximate the triplet energy, but the UMP series for M = 0 shows no sign of converging to the value obtained using M = 1. The O-2 and CH2 molecules are treated as examples.