This application provides azeotropic and near-azeotropic compositions of Z-1233zd and a second component selected from the group consisting of methyl formate, dimethoxymethane, HFC-43-10-mee and HFC-245fa. The inventive compositions are useful as aerosol propellants, refrigerants, cleaning agents, expansion agents for thermoplastic and thermoset foams, solvents, heat transfer media, gaseous dielectrics, fire extinguishing and suppression agents, power cycle working fluids, polymerization media, particulate removal fluids, carrier fluids, buffing abrasive agents, and displacement drying agents. The compositions were modeled based on Vapor-Liquid Equilibria data such as those illustrated in the figures.