We report a zero-field optically detected magnetic resonance study under high pressure for triplet pyrimidine in benzene, pyrazine in benzene and in p-dichlorobenzene, and s-tetramethylpyrazine in durene. Generally the pressure sensitivity of the zero-field splitting (ZFS) parameter D, partial derivative D/partial derivative P, for these compounds is much higher than that for quinoxaline. This is rationalized in terms of a smaller pi-electron cloud in the monocyclics than in quinoxaline. For pyrazine and pyrimidine, the (3)n pi* nature of the lowest triplet leads to a larger spin-orbit contribution to the pressure shift. We observed a larger change in the ZFS parameter E for pyrazine in benzene than in dichlorobenzene. This is explained by the difference in crystalline packing between the two host lattices. There is a large change in D and a multiplet splitting under high pressure for tetramethylpyrazine. These are ascribed to the presence of a pseudo-Jahn-Teller interaction in this molecule.