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Motivation Cortical bone is an important contributor to bone strength and is pivotal to understand the etiology of osteoporotic fractures and the specific mechanisms of antiosteoporotic treatment regimen. 3D computed tomography (CT) can be used to measure cortical thickness, density, and mass in the proximal femur, lumbar vertebrae, and distal forearm. However, the spatial resolution of clinical whole body CT scanners is limited by radiation exposure; partial volume artefacts severely impair the accurate assessment of cortical parameters, in particular in locations where the cortex is thin such as in the lumbar vertebral bodies or in the femoral neck. Method Model-based deconvolution approaches recover the cortical thickness by numerically deconvolving the image along 1D profiles using an estimated scanner point spread function (PSF) and a hypothesized uniform cortical bone mineral density (reference density). In this work we provide a new essentially analytical unique solution to the model-based cortex recovery problem using few characteristics of the measured profile and thus eliminate the non-linear optimization step for deconvolution. Also, the proposed approach allows to get rid of the PSF in the model and reduces sensitivity to errors in the reference density. Additionally, run-time and memory effective computation of cortical thickness was achieved with the help of a lookup table. Results The method accuracy and robustness was validated and compared to that of a deconvolution approach recently proposed for cortical bone and of the 50% relative threshold technique: in a simulated environment with noise and various error levels in the reference density and using CT acquisitions of the European Forearm Phantom (EFP II), a modification of a widely used anthropomorphic standard of cortical and trabecular bone compartments that was scanned with various scan protocols. Conclusion Results of simulations and of phantom data analysis verified the following properties of the new method: 1) Robustness against errors in the reference density. 2) Excellent accuracy on ground truth data with various noise levels. 3) Very fast computation using a lookup table.