Linear regularization using statistical information or solution simplicity as stabilizing functional has been examined for inversions of atmospheric radiometric measurements. Statistical regularization is commonly known as the optimal estimation method (OEM), while the latter approach is often denoted as Tikhonov regularization (TR). The study focuses on considerations and parameters important for the methods in order to obtain a close to optimal inversion accuracy, here defined as the lowest possible total retrieval error. Two criteria to determine a suitable value for the Tikhonov regularization parameter, the discrepancy principle and the L curve, have been extended to handle ensemble retrievals. The natural variance implied by the solution measure selected for TR, and the importance for OEM to consider uncertainties of the assumed mean profile, are discussed. Detailed simulations of ground-based ozone measurements around 110.8 GHz have been used to derive more specific results. For such observations, both methods can give a close to optimal performance, but the problems to address differ. TR needs fewer basic considerations but more circumstantial calculations, while OEM uses statistical information of natural variability, which is a drawback when this quantity is poorly known. The assumed vertical correlation is shown to be a critical retrieval parameter for both methods.