Copper-catalyzed reactions of terminal 1,3-diynes with electron-deficient azides to generate either 3-alkynyl or 2,3-dienyl imidamides and imidates are described. The selectivity depends on the diyne substituents and the nucleophile that reacts with the ketenimide intermediate generated from the corresponding triazole precursor. Reactions of 1,3-diynes containing a propargylic acetate afford [3]cumulenyl imidamides, while reactions using methanol as the trapping agent selectively generate 2,3-dienyl imidates. Five-membered heterocycles were obtained from 1,3-diynes containing a homopropargylic hydroxyl or amine substituent.