The cycloaddition of azides to iodoalkynes is strongly enhanced by some Cu+-complexes. We have studied computationally six reaction pathways for the cycloaddition of 24 combinations of azide and iodoalkyne to identify the dominant pathways and the influence of reactant structure on the evolution of the reaction. Two pathways were found to be operating for distinct sets of reactants. In the first pathway, initial complexation of iodoalkyne by Cu+ is followed by the binding of the azide to the metal through its substituted nitrogen atom, followed by attack of the nonhalogenated alkyne carbon by the terminal nitrogen atom. This pathway is generally followed by aromatic or electron-deficient azides, unless the iodoalkyne bears an electron-withdrawing group. The second pathway is a single-step mechanism similar (apart from the alkyne bond weakening caused by complexation) to that observed in the absence of catalyst. Electron-deficient iodoalkynes and methyl azides strongly prefer this mechanism, regardless of the identity of the reaction partners. The catalytic gain obtained through the use of Cu+ depends only partially on its direct effect on the energy of the transition state (relative to that of the infinitely separated reactants) and may be lost if the iodoalkyne itself strongly interacts with the catalyst through the formation of too strong a pi-complex.