Methods for the conditioning of bioprosthetic material employ bovine pericardial membrane. A laser directed at the fibrous surface of the membrane and moved relative thereto reduces the thickness of the membrane to a specific uniform thickness and smoothes the surface. The wavelength, power and pulse rate of the laser are selected which will smooth the fibrous surface as well as ablate the surface to the appropriate thickness. Alternatively, a dermatome is used to remove a layer of material from the fibrous surface of the membrane. Thinning may also employ compression. Stepwise compression with cross-linking to stabilize the membrane is used to avoid damaging the membrane through inelastic compression. Rather, the membrane is bound in the elastic compressed state through addition cross-linking. The foregoing several thinning techniques may be employed together to achieve strong thin membranes.