We apply the D3 dispersion correction to the exchange–correlation functionals of the TCA family, namely TCA and RevTCA, and assess their performance for various solid-state problems (bulk solids, noble gases, molecular crystals). We find that the dispersion-corrected versions TCA+D3 and RevTCA+D3 yield a consistent good performance for all the examined problems, being competitive with other state of the art generalized gradient approximations. This result is particularly remarkable because the D3 correction could be applied with minimal or no modifications with respect to the previous molecular investigations, where RevTCA+D3 and TCA+D3 proved to be very good. This means that TCA+D3 and RevTCA+D3 are efficient, well balanced, and widely applicable tools for general electronic-structure applications.