A series of experiments have been carried out on the influence of additives on the crystal growth and superconductivity of YBa2Cu3O7-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 x 10 x 0.5 or 12 x 10 x 1 mm(3) 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.