A method for producing bubble-free glasses is provided, in which a glass mixture that is arsenic-free and antimony-free with the exception of any unavoidable raw material impurities and a sulfate compound and SnO2 as refining agents are used. The glass mixture is melted and primarily refined in a first region of a melting tank, an average melting temperature (T1) is set at T1>1560° C. and an average melt residence time (t1) is set at t1>2 hours. The proportion of SO3 resulting from the decomposition of the sulfate compound is reduced to less than 0.002 wt. % as the primary refinement is carried out. A secondary refinement is carried out in a second region of the melting tank, an average melting temperature (T2) is set at T2>1640° C. and an average melt residence time (t2) is set at t2>1 hour.