We have drawn the phase diagram of tetragonal Fe1+xTe1-ySeyFe1+xTe1-ySey based on the investigations carried on single-crystalline samples for y⩽0.5y⩽0.5. Sizeable single-crystals were grown by self-flux melting in vacuum-sealed reactors and characterized by X-ray diffraction, electron microscopy, magnetic and transport measurements. Contrary to previous studies on polycrystalline samples, we found the magnetic transition to disappear only close to y=0.5y=0.5, whereas superconductivity is found to occur at y⩾0.45y⩾0.45. Above a given threshold, strong electron correlations become detrimental to the appearance of superconductivity in this family of compounds. The appearance of superconductivity is favored at lower Se content by decreasing the Fe excess x . Highly pure superconducting crystals were grown starting from the nominal composition Fe0.9Te0.7Se0.3Fe0.9Te0.7Se0.3.