According to the maintenance hypothesis (Nyberg et al., 2012), structural integrity of the brain’s grey matter helps to preserve cognitive functioning into old age. A corollary of this hypothesis that can be tested in cross-sectional data is that grey-matter structural integrity and general cognitive ability are positively associated in old age. Building on Köhncke et al. (2021), who found that region-specific latent factors of grey-matter integrity are positively associated with episodic memory ability among older adults, we examine associations between general factors of grey-matter integrity and a general factor of cognitive ability in a cross-sectional sample of 1466 participants aged 60–88 years, 319 of whom contributed imaging data. Indicator variables based on T1-weighted images (voxel-based morphometry, VBM), magnetization-transfer imaging (MT), and diffusion tensor imaging-derived mean diffusivity (MD) had sufficient portions of variance in common to establish latent factors of grey-matter structure for a comprehensive set of regions of interest (ROI). Individual differences in grey-matter factors were positively correlated across neocortical and limbic areas, allowing for the definition of second-order, general factors for neocortical and limbic ROI, respectively. Both general grey-matter factors were positively correlated with general cognitive ability. For the basal ganglia, the three modality-specific indicators showed heterogenous loading patterns, and no reliable associations of the general grey-matter factor to general cognitive ability were found. To provide more direct tests of the maintenance hypothesis, we recommend applying the present structural modeling approach to longitudinal data, thereby enhancing the physiological validity of latent constructs of brain structure.