The European Space Agency (ESA) Earth Explorer Mission Aeolus was launched in August 2018, carrying the first Doppler wind lidar in space. Its primary payload, the Atmospheric LAser Doppler INstrument (ALADIN), is an ultraviolet (UV) high-spectral-resolution lidar (HSRL) measuring atmospheric backscatter from air molecules and particles in two separate channels. The primary mission product is globally distributed line-of-sight wind profile observations in the troposphere and lower stratosphere. Atmospheric optical properties are provided as a spin-off product. Being an HSRL, Aeolus is able to independently measure the particle extinction coefficients, co-polarized particle backscatter coefficients and the co-polarized lidar ratio (the cross-polarized return signal is not measured). This way, the retrieval is independent of a priori lidar ratio information. The optical properties are retrieved using the standard correct algorithm (SCA), which is an algebraic inversion scheme and therefore sensitive to measurement noise. In this work, we reformulate the SCA into a physically constrained maximum-likelihood estimation (MLE) problem and demonstrate a predominantly positive impact and considerable noise suppression capabilities. These improvements originate from the use of all available information by the MLE in conjunction with the expected physical bounds concerning positivity and the expected range of the lidar ratio. To consolidate and to illustrate the improvements, the new MLE algorithm is evaluated against the SCA on end-to-end simulations of two homogeneous scenes and for real Aeolus data collocated with measurements by a ground-based lidar and the Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) satellite. The largest improvements were seen in the retrieval precision of the extinction coefficients and lidar ratio ranging up to 1 order of magnitude or more in some cases due to effective noise dampening. In real data cases, the increased precision of MLE with respect to the SCA is demonstrated by increased horizontal homogeneity and better agreement with the ground truth, though proper uncertainty estimation of MLE results is challenged by the constraints, and the accuracy of MLE and SCA retrievals can depend on calibration errors, which have not been considered.