The utility of a Hartree–Fock triplet stability threshold, for identifying time-dependent density functional theory triplet excitations for which the inclusion of exact orbital exchange is detrimental, is illustrated for a benchmark set of 63 excitations in 20 organic molecules. Following earlier spin–spin coupling observations that suggest a relatively small triplet instability problem, the accuracy of triplet excitation energies from the B97-2 hybrid functional is also quantified. As anticipated, the results are relatively accurate and this is readily understood in terms of the stabilities. Application of the Tamm–Dancoff approximation dramatically improves all the triplet excitation energies corresponding to low stabilities, whilst also providing a modest improvement in the corresponding singlet states.