Optimal estimation retrieval is a form of nonlinear regression which determines the most probable circumstances that produced a given observation, weighted against any prior knowledge of the system. This paper applies the technique to the estimation of aerosol backscatter and extinction (or lidar ratio) from two-channel Raman lidar observations. It produces results from simulated and real data consistent with existing Raman lidar analyses and additionally returns a more rigorous estimate of its uncertainties while automatically selecting an appropriate resolution without the imposition of artificial constraints. Backscatter is retrieved at the instrument's native resolution with an uncertainty between 2 and 20%. Extinction is less well constrained, retrieved at a resolution of 0.1–1 km depending on the quality of the data. The uncertainty in extinction is > 15%, in part due to the consideration of short 1 min integrations, but is comparable to fair estimates of the error when using the standard Raman lidar technique. <br><br> The retrieval is then applied to several hours of observation on 19 April 2010 of ash from the Eyjafjallajökull eruption. A depolarising ash layer is found with a lidar ratio of 20–30 sr, much lower values than observed by previous studies. This potentially indicates a growth of the particles after 12–24 h within the planetary boundary layer. A lower concentration of ash within a residual layer exhibited a backscatter of 10 Mm<sup>−1</sup> sr<sup>−1</sup> and lidar ratio of 40 sr.