Functional neuroimaging studies report increased right prefrontal cortex (PFC) involvement during verbal memory tasks amongst low-scoring older individuals, compared to younger controls and their higher-scoring contemporaries. Some propose that this reflects inefficient use of neural resources through failure of the left PFC to inhibit non-task-related right PFC activity, via the anterior corpus callosum (CC). For others, it indicates partial compensation – that is, the right PFC cannot completely supplement the failing neural network, but contributes positively to performance. We propose that combining structural and diffusion brain MRI can be used to test predictions from these theories which have arisen from fMRI studies. We test these hypotheses in immediate and delayed verbal memory ability amongst 90 healthy older adults of mean age 73 years. Right hippocampus and left dorsolateral prefrontal cortex (DLPFC) volumes, and fractional anisotropy (FA) in the splenium made unique contributions to verbal memory ability in the whole group. There was no significant effect of anterior callosal white matter integrity on performance. Rather, segmented linear regression indicated that right DLPFC volume was a significantly stronger positive predictor of verbal memory for lower-scorers than higher-scorers, supporting a compensatory explanation for the differential involvement of the right frontal lobe in verbal memory tasks in older age.