People with larger brains tend to score higher on tests of general intelligence (g). It is unclear, however, how much variance in intelligence other brain measurements would account for if included together with brain volume in a multivariable model. We examined a large sample of individuals in their seventies (n = 672) who were administered a comprehensive cognitive test battery. Using structural equation modelling, we related six common magnetic resonance imaging-derived brain variables that represent normal and abnormal features—brain volume, cortical thickness, white matter structure, white matter hyperintensity load, iron deposits, and microbleeds—to g and to fluid intelligence. As expected, brain volume accounted for the largest portion of variance (~ 12%, depending on modelling choices). Adding the additional variables, especially cortical thickness (+~ 5%) and white matter hyperintensity load (+~ 2%), increased the predictive value of the model. Depending on modelling choices, all neuroimaging variables together accounted for 18–21% of the variance in intelligence. These results reveal which structural brain imaging measures relate to g over and above the largest contributor, total brain volume. They raise questions regarding which other neuroimaging measures might account for even more of the variance in intelligence.