A method for producing bubble-free glasses is provided, in which a glass mixture that is arsenic-free, antimony-free and tin-free with the exception of any unavoidable raw material impurities and at least one sulfate compound as a refining agent are used. The glass mixture and refining agent are melted and primarily refined in a first region of a melting tank, an average melting temperature (T1) is set at T1>1580° C. and an average melt residence time (t1) is set at t1>2 hours. A secondary refinement is carried out in a second region, an average melting temperature (T2) is set at T2>1660° C. and an average melt residence time (t2) is set at t2>1 hour, and the proportion of the SO3 resulting from decomposition of the sulfate is reduced to less than 0.002 wt. %.