A series of experiments have been carried out on the influence of additives on the crystal growth and superconductivity of YBa₂Cu₃O_{7- delta} (YBCO) crystals grown in alumina crucibles from the eutectic self-flux system of BaO-CuO. The single additives were B₂O₃, Bi₂O₃, BaF₂ or BaCl₂ and the double additives were BaF₂-B₂O₃ or BaF₂-Bi₂O₃. It was found that a small amount of BaF₂ greatly improved not only the crystal growth, by increasing solute solubility and crystal yield, but also the superconductivity by reducing Al contamination and resulting in a chemical composition approaching stoichiometry. As a result, single crystals up to 20*10*0.5 or 12*10*1 mm³ in size have been obtained, and a superconducting transition temperature of 92.5 K with a transition width of 1 K in the as-grown state, or T_c=93 K with transition width <1 K after annealing in oxygen have been reached by using BaF₂ as additive. A model is proposed to interpret these improvements: it incorporates F^- induced monomolecular clusters in the high-temperature solution and preferential adsorption of F^- on the surface of the growing crystal.