The single-molecule conductance of saturated molecules can potentially be fully suppressed by destructive quantum interference in their σ-system. However, only few molecules with σ-interference have been identified and the structure-property relationship remains to be elucidated. Here, we explore the role of substituents in modulating the electronic transmission of saturated molecules. In functionalized bicyclo[2.2.2]octanes, the transmission is suppressed by σ- interference when fluorine substituents are applied. For bicyclo[2.2.2]octasilane and - octagermanes the transmission is suppressed when carbon-based substituents are used, and such molecules are likely to be highly insulating. For the carbon-based substituents we find a strong correlation between the appropriate Hammett constants and the transmission. The substituent effect enables systematic optimization of the insulating properties of saturated molecular cores.