On the basis of a known method for producing a blank of titanium-doped glass with a high silica content (glass) for a mirror substrate for use in EUV lithography which has a surface region that has an outer contour, is intended to be provided with a reflective coating and is specified as a highly loaded zone when the mirror substrate is used as intended, in order to provide a blank which can be produced at low cost and nevertheless meets high requirements with respect to homogeneity and freedom from blisters and striae, a procedure which comprises the following method steps is proposed: (a) producing a front body of titanium-doped high-quality glass with dimensions more than large enough to enclose the outer contour, (b) producing a cylindrical supporting body from titanium-doped glass, (c) bonding the front body and the supporting body to form a composite body, and (d) working the composite body to form the mirror substrate blank, wherein the step of producing the front body comprises a homogenizing process involving twisting a starting body obtained in the form of a strand by flame hydrolysis of a silicon-containing compound to form a front body blank, and the supporting body is formed as a monolithic glass block with less homogeneity than the front body.