Quantum calculations are used to examine the properties of heterodimers formed by a series of tetrel-containing molecules with NH as universal Lewis base. TH was taken as a starting point, with T = C, Si, Ge, and Sn. The H atoms were replaced by various numbers of F atoms-THF, TFH, and TF-so as to monitor the effects of adding electron-withdrawing substituents. Unsubstituted TH molecules form the weakest tetrel bonds, only up to about 2 kcal/mol. The bond is strengthened when the H opposite NH is replaced by F, rising up to the 6-9 kcal/mol range. Another means of strengthening arises when the three peripheral H atoms of TH are replaced by F. The effect of the latter is heavily dependent on the nature of the T atom and is particularly noticeable for larger tetrels. The two sorts of fluorination patterns are cooperative, in that their combination in TF yields by far the most powerful tetrel bonding agent. The tetrel bond is strengthened as the T atom moves further down the periodic table column. The strongest bond amounts to 25.5 kcal/mol for SnF··NH. A number of features correlate with the binding energy, but only roughly. These properties include the charge transfer, the AIM bond critical point electron density, the molecular electrostatic potential, and the stretch of the T-X covalent bond upon complex formation.