The equation that relates the rotational speed to the wall shear stresses in Couette viscometers is treated as an integral equation of the first kind for the unknown shear stress versus shear rate function and the wall shear stress versus slip velocity function. A method, based on Tikhonov regularization, is used to obtain approximate solutions of these two material property functions simultaneously. To determine the slip velocity function data from two or more Couette viscometers with different radii are required but, unlike existing methods, there are no restrictions on the radius ratios of these viscometers. This way of processing Couette viscometry data also does not require the functional forms of the material functions to be prescribed. The built-in regularization parameter of Tikhonov regularization keeps noise amplification under control giving material property functions that are relatively free of spurious fluctuations. The performance of this method of treating Couette viscometry data is demonstrated by applying it to a number of data sets taken from the published literature. (C) 2004 Elsevier B.V. All rights reserved.