Tris(heterocyclemethyl)amines containing mixtures of 1,2,3-triazolyl, 2-benzimidazoyl, and 2-pyridyl components were prepared for ligand acceleration of the copper-catalyzed azide-alkyne cycloaddition reaction. Two classes of ligands were identified: those that give rise to high reaction rates in coordinating solvents but inhibit the process when used in excess relative to copper and those that provide for fast catalysis in water and are not inhibitory in excess. Several "mixed" ligands were identified that performed well under both types of conditions. Kinetics measurements as a function of ligand:metal ratio and catalyst concentration were found to be consistent with an active Cu2L formulation. Since strongly bound chelating agents are not always the most effective, achieving optimal rates requires an assessment of the potential donor molecules in the reaction mixture. Simple rules are provided to guide the user in the choice of effective ligands and reaction conditions to suit most classes of substrates, solvents, and concentrations.