The development and application of predictive models for organic electronic devices with a complex layer structure, such as white organic light-emitting diodes, require the availability of an accurate and fast method for extracting the materials parameters, which determine the mobility in each of the layers from a set of experimental data. The absence of such a generally used method may be regarded as one of the reasons why so far relatively little consensus has been obtained concerning the most appropriate transport model, the shape of the density of states (DOS), and the underlying microscopic parameters, such as the width of the DOS and the density of hopping sites. In this paper, we present a time-efficient Gauss-Newton method for extracting these parameters from current-voltage curves for single-carrier devices, obtained for various layer thicknesses and temperatures. The method takes the experimental uncertainties into account and provides the correlated uncertainty margins of the parameters studied. We focus on materials with a Gaussian DOS with random and spatially correlated disorder. Making use of artificially generated as well as experimental data sets, we demonstrate the accuracy and limitations, and show that it is possible to deduce the type of disorder from the analysis. The presence of an exponential trap DOS, as is often observed for the case of electron transport, is found to significantly reduce the accuracy of the transport parameters obtained.