The trans influence of various X ligands in hypervalent iodine(III) complexes of the type CF3[I(X)Cl] has been quantified using the trans I-Cl bond length (d(X)), the electron density rho(r) at the (3, -1) bond critical point of the trans I-Cl bond, and topological features of the molecular electrostatic potential (MESP). The MESP minimum at the Cl lone pair region (V-min) is a sensitive measure of the trans influence. The trans influence of X ligands in hypervalent iodine(V) complexes is smaller than that in iodine(III) complexes, while the relative ordering of this influence is the same in both complexes. In CF3[I(X)Y] complexes, the mutual trans influence due to the trans disposition of the X and Y ligands is quantified using the energy E-XY of the isodesmic reaction CF3[I(X)Cl] + CF3[I(Y)Cl] -> CF3[I(Cl)Cl] + CF3[I(X)Y]. E-XY is predicted with good accuracy using the trans-influence parameters of X and Y, measured in terms of d(X), rho(r), or V-min. The bond dissociation energy (E-d) of X or Y in CF3[I(X)Y] is significantly influenced by the trans influence as well as the mutual trans influence. This is confirmed by deriving an empirical equation to predict Ed using one of the trans-influence parameters (d(X), rho(r), or V-min) and the mutual trans-influence parameter E-XY for a large number of complexes. The quantified values of both the trans influence and the mutual trans-influence parameters may find use in assessing the stability of hypervalent iodine compounds as well as in the design of new stable hypervalent complexes. Knowledge about the I-X bond dissociation energies will be useful for explaining the reactivity of hypervalent iodine complexes and the mechanism of their reactions.