Past investigations of membrane mirrors have led to the conclusion that they are not suitable for imaging in the visible. We reexamine this conclusion and discuss ways to circumvent the principal problems. A reanalysis of l'Garde measurements of a 6-^m-thick membrane mirror corrects earlier interpretations of the "W curve'' asymmetry. Correction of the classical Hencky aspheric shape of membrane mirrors is required to upgrade them for use in visible passbands. The theory of variable membrane thickness in a radial direction is presented. A numerical integration is done and a unique quadratic radial variation of thickness is found that corrects for the u4 Hencky term. Two methods to fabricate such a membrane are presented.